1
AIR JEE Main (2026)
Motion in a plane
Most Important JEE PYQs
Single Correct Type Questions 4. A projectile is projected at 30° from horizontal with initial
velocity 40 ms–1. The velocity of the projectile at t = 2 s
1. The initial speed of a projectile fired from ground is u. At from the start will be:
the highest point during its motion, the speed of projectile (Given g = 10 m/s2) [11 April, 2023 (Shift-II)]
3
is u. The time of flight of the projectile is: (a) 20 3 ms −1
2
[31 Jan, 2023 (Shift-I)]
(b) 40 3 ms −1
u u (c) 20 ms–1
(a) (b)
2g g (d) Zero
5. Two projectiles are projected at 30° and 60° with the
2u 3u horizontal with the same speed. The ratio of the maximum
(c) (d)
g g height attained by the two projectiles respectively is:
2. The trajectory of projectile, projected from the ground is [10 April, 2023 (Shift-II)]
x2 (a) 2 : 3
given by y= x − . Where x and y are measured in
20 (b) 3 :1
meter. The maximum height attained by the projectile will (c) 1 : 3
be. [8 April, 2023 (Shift-II)]
(d) 1: 3
(a) 5 m (b) 10 2 m 6. The maximum vertical height to which a man can throw
a ball is 136 m. The maximum horizontal distance upto
(c) 200 m (d) 10 m which he can throw the same ball is
3. For a body projected at an angle with the horizontal from [24 Jan, 2023 (Shift-I)]
the ground, choose the correct statement. (a) 192 m
(b) 136 m
[1 Feb, 2023 (Shift-II)] (c) 272 m
(a) Gravitational potential energy is maximum at the (d) 68 m
highest point. 7. A projectile is launched at an angle ‘a’ with the horizontal
(b) The horizontal component of velocity is zero at with a velocity 20 ms. After 10 s, it inclination with
horizontal is ‘b’. The value of tan b will be: (g = 10 ms–2).
highest point.
[27 June, 2022 (Shift-I)]
(c) The vertical component of momentum is maximum
(a) tana + 5seca
at the highest point.
(b) tana – 5seca
(d) The kinetic energy (K.E.) is zero at the highest point (c) 2 tanα – 5seca
of projectile motion. (d) 2tana + 5seca
, 2
8. A body of mass 10 kg is projected at an angle of 45° with 1 5 −1
the horizontal. The trajectory of the body is observed to (b) θ0 =sin −1 and ν 0 = ms
pass through a point (20, 10). If T is the time of flight, 5 3
T 3 −1
then its momentum vector, at time t = is______ 2
2 (c) θ0 =sin −1 and ν 0 =5 ms
5
[Take g = 10 m/s2 ] [27 July, 2022 (Shift-II)]
5 −1
(
(a) 100 iˆ + 100 2 − 200 ˆj ) 1
(d) θ0 =cos −1 and ν 0 =3 ms
5
(
(b) 100 2 iˆ + 100 − 200 2 ˆj ) 14. A stone is projected at angle 30o to the horizontal. The
(
(c) 100 iˆ + 100 − 200 2 ˆj ) ratio of kinetic energy of the stone at point of projection
to its kinetic energy at the highest point of flight will be
(
(d) 100 2 iˆ + 100 2 − 200 ˆj ) [29 Jan, 2023 (Shift-I)]
9. A projectile is projected with velocity of 25 m/s at an angle θ (a) 1 : 2 (b) 1 : 4
with the horizontal. After t seconds its inclination with (c) 4 : 1 (d) 4 : 3
horizontal becomes zero. If R represents horizontal range
15. A plane is inclined at an angle α = 30° with a respect
of the projectile, the value of θ will be: to the horizontal. A particle is projected with a speed
[Use g = 10 m/s2] [24 June, 2022 (Shift-I)] u = 2 ms–1 from the base of the plane, making an angle
θ = 15° with respect to the plane as shown in the figure.
1 −1 5t 2 1 −1 4 R The distance from the base, at which the particle hits the
(a) sin (b) sin 2
2 4R 2 5t plane is close to: [10 April, 2019 (Shift-II)]
(Take g = 10 ms )–2
−1 4t
2
−1 R
(c) tan (d) cot
5R 20t 2
10. A person can throw a ball upto a maximum range of 100
m. How high above the ground he can the same ball?
º
15
=
[29 June, 2022 (Shift-II)] u
= 30º
(a) 25 m (b) 50 m
(c) 100 m (d) 200 m (a) 14 cm (b) 20 cm
11. A body is projected at t = 0 with a velocity 10 ms at an –1 (c) 18 cm (d) 26 cm
angle of 60° with the horizontal. The radius of curvature 16. A passenger sitting in a train A moving at 90 km/h observes
of its trajectory at t = 1 s is R. Neglecting air resistance and another train B moving in the opposite direction for 8 s. If
taking acceleration due to gravity g = 10 ms–2 the radius the velocity of the train B is 54 km/h, then length of train
of R is: [11 Jan, 2019 (Shift-I)] B is: [13 April, 2023 (Shift-II)]
(a) 10.3 m (b) 2.8 m (a) 80 m (b) 200 m
(c) 2.5 m (d) 5.1 m (c) 120 m (d) 320 m
12. A shell is fired from a fixed artillery gun with an initial 17. Two buses P and Q start from a point at the same time and
speed u such that it hits the target on the ground at a move in a straight line and their positions are represented
distance R from it. If t1 and t2 are the values of the time by Xp(t) = αt + βt2 and XQ (t) = ft – t2. At what time, both
taken by it to hit the target in two possible ways, the product the buses have same velocity? [25 June, 2022 (Shift-II)]
t1t2 is: [12 April, 2019 (Shift-I)] (a) α − f
(a) R/g (b) R/4g 1+ β
(c) 2R/g (d) R/2g α+ f
(b)
13. The trajectory of a projectile near the surface of the earth 2 ( β − 1)
is given as y = 2x – 9x2 . If it were launched at an angle θ0 with
α+ f
speed ν0 then (g =10 ms–2) [12 April, 2019 (Shift-I)] (c)
2 (1 + β )
2 3 −1
(a) θ0 =cos −1 and ν 0 =5 ms f −α
5 (d)
2 (1 + β )
, 3
18. Train A and train B are running on parallel tracks in (a) ω ( R1 + R2 ) iˆ
opposite directions with speeds of 36 km/hour and 72 km/
hour, respectively, A person is walking in train A in the (b) −ω ( R1 + R2 ) iˆ
direction opposite to its motion with a speed of 1.8 km/
hour. Speed (in ms–1) of this person as observed from train (c) ω ( R2 − R1 ) iˆ
B will be close to: (take the distance between the tracks
as negligible) [2 Sep, 2020 (Shift-I)] (d) ω ( R1 − R2 ) iˆ
(a) 28.5 ms–1 (b) 31.5 ms–1
(c) 30.5 ms–1 (d) 29.5 ms–1 Integer Type Questions
19. A particle is moving with a velocity
= v K ( yiˆ + xjˆ) , where 23. If the initial velocity in horizontal direction of a projectile
is unit vector î and the equation of trajectory is y = 5x(1 – x).
K is a constant. The general equation for its path is:
The y component vector of the initial velocity is
[9 Jan, 2019 (Shift-I)] _________ ĵ.
(a) y = x2 + constant (Take g = 10 m/s2) [26 July, 2022 (Shift-I)]
(b) y2 = x + constant 24. An object is projected in the air with initial velocity u at an
angle θ. The projectile motion is such that the horizontal
(c) y2 = x2 + constant
range R, is maximum. Another object is projected in the
(d) xy = constant air with a horizontal range half of the range of first object.
20. The stream of a river is flowing with a speed of 2km/h. A The initial velocity remains same in both the case. The
swimmer can swim at a speed of 4km/h. What should be value of the angle of projection, at which the second object
the direction of the swimmer with respect to the flow of is projected, will be ____________ degree.
the river to cross the river straight? [29 July, 2022 (Shift-I)]
[9 April, 2019 (Shift-I)] 25. If the initial velocity in horizontal direction of a projectile is
(a) 60° (b) 150° unit vector iˆ and the equation of trajectory is y = 5x (l – x).
(c) 90° (d) 120° The y component vector of the initial velocity is ______ ĵ
21. Two projectile thrown at 30° and 45° with the horizontal (Take g = 10 m/s2 ) [JEE Adv, 2022]
respectively, reach the maximum height in same time. The
26. A fighter jet is flying horizontally at a certain with a
ratio of their initial velocities is[26 July, 2022 (Shift-I)]
speed of 200 ms–1.When it passes directly overhead ad
(a) 1: 2 (b) 2 : 1 anti-aircraft gun, a bullet is fired from the gun, at an angle
θ with the horizontal, to hit the jet. If the bullet speed is
(c) 2 :1 (d) 1 : 2 400 m/s, the value of θ will be __________.
[26 June, 2022 (Shift-I)]
22. Two particles A, B are moving on two concentric circles
of radii R1 and R2 with equal angular speed ω. At t = 0, 27. A swimmer wants to cross a river from point A to point
their positions and direction of motion are shown in the B. Line AB makes an angle of 30° with the flow of river.
Magnitude of velocity of the swimmer is same as that
figure: [12 Jan, 2019 (Shift-II)]
Y of the river. The angle θ with the line AB should be
_________ °, so that the swimmer reaches point B.
[27 July, 2021 (Shift-II)]
A
B
R1 X
B
R2
θ
π 30°
The relative velocity v A − vB at t = is given by:
2ω A
, 4
28. A particle is moving along the x-axis with its coordinate 30. An object is projected in the air with initial velocity u at an
with time ‘t’ given by x(t) = 10 + 8t – 3t2. Another particle angle q. The projectile motion is such that the horizontal
is moving along the y-axis with its coordinate as a function range R, is maximum. Another object is projected in the
of time given by y(t) = 5 – 8t3. At t = 1s, the speed of
air with a horizontal range half of the range of first object.
the second particle as measured in the frame of the first
The initial velocity remains same in both the case. The
particle is given as v . Then v(in m/s) is
value of the angle of projection, at which the second object
[8 Jan, 2020 (Shift-I)]
is projected, will be ________degree.(Mark the smallest
29. A ball of mass m is thrown vertically upward. Another ball
of mass 2 m is thrown an angle θ with the vertical. Both the angle possible) [JEE Adv, 2022]
balls stay in air for the same period of time. The ratio of
1
the heights attained by the two balls respectively is . The
x
value of x is __________. [JEE Adv, 2022]
PW Web/App - https://smart.link/7wwosivoicgd4
Library- https://smart.link/sdfez8ejd80if
AIR JEE Main (2026)
Motion in a plane
Most Important JEE PYQs
Single Correct Type Questions 4. A projectile is projected at 30° from horizontal with initial
velocity 40 ms–1. The velocity of the projectile at t = 2 s
1. The initial speed of a projectile fired from ground is u. At from the start will be:
the highest point during its motion, the speed of projectile (Given g = 10 m/s2) [11 April, 2023 (Shift-II)]
3
is u. The time of flight of the projectile is: (a) 20 3 ms −1
2
[31 Jan, 2023 (Shift-I)]
(b) 40 3 ms −1
u u (c) 20 ms–1
(a) (b)
2g g (d) Zero
5. Two projectiles are projected at 30° and 60° with the
2u 3u horizontal with the same speed. The ratio of the maximum
(c) (d)
g g height attained by the two projectiles respectively is:
2. The trajectory of projectile, projected from the ground is [10 April, 2023 (Shift-II)]
x2 (a) 2 : 3
given by y= x − . Where x and y are measured in
20 (b) 3 :1
meter. The maximum height attained by the projectile will (c) 1 : 3
be. [8 April, 2023 (Shift-II)]
(d) 1: 3
(a) 5 m (b) 10 2 m 6. The maximum vertical height to which a man can throw
a ball is 136 m. The maximum horizontal distance upto
(c) 200 m (d) 10 m which he can throw the same ball is
3. For a body projected at an angle with the horizontal from [24 Jan, 2023 (Shift-I)]
the ground, choose the correct statement. (a) 192 m
(b) 136 m
[1 Feb, 2023 (Shift-II)] (c) 272 m
(a) Gravitational potential energy is maximum at the (d) 68 m
highest point. 7. A projectile is launched at an angle ‘a’ with the horizontal
(b) The horizontal component of velocity is zero at with a velocity 20 ms. After 10 s, it inclination with
horizontal is ‘b’. The value of tan b will be: (g = 10 ms–2).
highest point.
[27 June, 2022 (Shift-I)]
(c) The vertical component of momentum is maximum
(a) tana + 5seca
at the highest point.
(b) tana – 5seca
(d) The kinetic energy (K.E.) is zero at the highest point (c) 2 tanα – 5seca
of projectile motion. (d) 2tana + 5seca
, 2
8. A body of mass 10 kg is projected at an angle of 45° with 1 5 −1
the horizontal. The trajectory of the body is observed to (b) θ0 =sin −1 and ν 0 = ms
pass through a point (20, 10). If T is the time of flight, 5 3
T 3 −1
then its momentum vector, at time t = is______ 2
2 (c) θ0 =sin −1 and ν 0 =5 ms
5
[Take g = 10 m/s2 ] [27 July, 2022 (Shift-II)]
5 −1
(
(a) 100 iˆ + 100 2 − 200 ˆj ) 1
(d) θ0 =cos −1 and ν 0 =3 ms
5
(
(b) 100 2 iˆ + 100 − 200 2 ˆj ) 14. A stone is projected at angle 30o to the horizontal. The
(
(c) 100 iˆ + 100 − 200 2 ˆj ) ratio of kinetic energy of the stone at point of projection
to its kinetic energy at the highest point of flight will be
(
(d) 100 2 iˆ + 100 2 − 200 ˆj ) [29 Jan, 2023 (Shift-I)]
9. A projectile is projected with velocity of 25 m/s at an angle θ (a) 1 : 2 (b) 1 : 4
with the horizontal. After t seconds its inclination with (c) 4 : 1 (d) 4 : 3
horizontal becomes zero. If R represents horizontal range
15. A plane is inclined at an angle α = 30° with a respect
of the projectile, the value of θ will be: to the horizontal. A particle is projected with a speed
[Use g = 10 m/s2] [24 June, 2022 (Shift-I)] u = 2 ms–1 from the base of the plane, making an angle
θ = 15° with respect to the plane as shown in the figure.
1 −1 5t 2 1 −1 4 R The distance from the base, at which the particle hits the
(a) sin (b) sin 2
2 4R 2 5t plane is close to: [10 April, 2019 (Shift-II)]
(Take g = 10 ms )–2
−1 4t
2
−1 R
(c) tan (d) cot
5R 20t 2
10. A person can throw a ball upto a maximum range of 100
m. How high above the ground he can the same ball?
º
15
=
[29 June, 2022 (Shift-II)] u
= 30º
(a) 25 m (b) 50 m
(c) 100 m (d) 200 m (a) 14 cm (b) 20 cm
11. A body is projected at t = 0 with a velocity 10 ms at an –1 (c) 18 cm (d) 26 cm
angle of 60° with the horizontal. The radius of curvature 16. A passenger sitting in a train A moving at 90 km/h observes
of its trajectory at t = 1 s is R. Neglecting air resistance and another train B moving in the opposite direction for 8 s. If
taking acceleration due to gravity g = 10 ms–2 the radius the velocity of the train B is 54 km/h, then length of train
of R is: [11 Jan, 2019 (Shift-I)] B is: [13 April, 2023 (Shift-II)]
(a) 10.3 m (b) 2.8 m (a) 80 m (b) 200 m
(c) 2.5 m (d) 5.1 m (c) 120 m (d) 320 m
12. A shell is fired from a fixed artillery gun with an initial 17. Two buses P and Q start from a point at the same time and
speed u such that it hits the target on the ground at a move in a straight line and their positions are represented
distance R from it. If t1 and t2 are the values of the time by Xp(t) = αt + βt2 and XQ (t) = ft – t2. At what time, both
taken by it to hit the target in two possible ways, the product the buses have same velocity? [25 June, 2022 (Shift-II)]
t1t2 is: [12 April, 2019 (Shift-I)] (a) α − f
(a) R/g (b) R/4g 1+ β
(c) 2R/g (d) R/2g α+ f
(b)
13. The trajectory of a projectile near the surface of the earth 2 ( β − 1)
is given as y = 2x – 9x2 . If it were launched at an angle θ0 with
α+ f
speed ν0 then (g =10 ms–2) [12 April, 2019 (Shift-I)] (c)
2 (1 + β )
2 3 −1
(a) θ0 =cos −1 and ν 0 =5 ms f −α
5 (d)
2 (1 + β )
, 3
18. Train A and train B are running on parallel tracks in (a) ω ( R1 + R2 ) iˆ
opposite directions with speeds of 36 km/hour and 72 km/
hour, respectively, A person is walking in train A in the (b) −ω ( R1 + R2 ) iˆ
direction opposite to its motion with a speed of 1.8 km/
hour. Speed (in ms–1) of this person as observed from train (c) ω ( R2 − R1 ) iˆ
B will be close to: (take the distance between the tracks
as negligible) [2 Sep, 2020 (Shift-I)] (d) ω ( R1 − R2 ) iˆ
(a) 28.5 ms–1 (b) 31.5 ms–1
(c) 30.5 ms–1 (d) 29.5 ms–1 Integer Type Questions
19. A particle is moving with a velocity
= v K ( yiˆ + xjˆ) , where 23. If the initial velocity in horizontal direction of a projectile
is unit vector î and the equation of trajectory is y = 5x(1 – x).
K is a constant. The general equation for its path is:
The y component vector of the initial velocity is
[9 Jan, 2019 (Shift-I)] _________ ĵ.
(a) y = x2 + constant (Take g = 10 m/s2) [26 July, 2022 (Shift-I)]
(b) y2 = x + constant 24. An object is projected in the air with initial velocity u at an
angle θ. The projectile motion is such that the horizontal
(c) y2 = x2 + constant
range R, is maximum. Another object is projected in the
(d) xy = constant air with a horizontal range half of the range of first object.
20. The stream of a river is flowing with a speed of 2km/h. A The initial velocity remains same in both the case. The
swimmer can swim at a speed of 4km/h. What should be value of the angle of projection, at which the second object
the direction of the swimmer with respect to the flow of is projected, will be ____________ degree.
the river to cross the river straight? [29 July, 2022 (Shift-I)]
[9 April, 2019 (Shift-I)] 25. If the initial velocity in horizontal direction of a projectile is
(a) 60° (b) 150° unit vector iˆ and the equation of trajectory is y = 5x (l – x).
(c) 90° (d) 120° The y component vector of the initial velocity is ______ ĵ
21. Two projectile thrown at 30° and 45° with the horizontal (Take g = 10 m/s2 ) [JEE Adv, 2022]
respectively, reach the maximum height in same time. The
26. A fighter jet is flying horizontally at a certain with a
ratio of their initial velocities is[26 July, 2022 (Shift-I)]
speed of 200 ms–1.When it passes directly overhead ad
(a) 1: 2 (b) 2 : 1 anti-aircraft gun, a bullet is fired from the gun, at an angle
θ with the horizontal, to hit the jet. If the bullet speed is
(c) 2 :1 (d) 1 : 2 400 m/s, the value of θ will be __________.
[26 June, 2022 (Shift-I)]
22. Two particles A, B are moving on two concentric circles
of radii R1 and R2 with equal angular speed ω. At t = 0, 27. A swimmer wants to cross a river from point A to point
their positions and direction of motion are shown in the B. Line AB makes an angle of 30° with the flow of river.
Magnitude of velocity of the swimmer is same as that
figure: [12 Jan, 2019 (Shift-II)]
Y of the river. The angle θ with the line AB should be
_________ °, so that the swimmer reaches point B.
[27 July, 2021 (Shift-II)]
A
B
R1 X
B
R2
θ
π 30°
The relative velocity v A − vB at t = is given by:
2ω A
, 4
28. A particle is moving along the x-axis with its coordinate 30. An object is projected in the air with initial velocity u at an
with time ‘t’ given by x(t) = 10 + 8t – 3t2. Another particle angle q. The projectile motion is such that the horizontal
is moving along the y-axis with its coordinate as a function range R, is maximum. Another object is projected in the
of time given by y(t) = 5 – 8t3. At t = 1s, the speed of
air with a horizontal range half of the range of first object.
the second particle as measured in the frame of the first
The initial velocity remains same in both the case. The
particle is given as v . Then v(in m/s) is
value of the angle of projection, at which the second object
[8 Jan, 2020 (Shift-I)]
is projected, will be ________degree.(Mark the smallest
29. A ball of mass m is thrown vertically upward. Another ball
of mass 2 m is thrown an angle θ with the vertical. Both the angle possible) [JEE Adv, 2022]
balls stay in air for the same period of time. The ratio of
1
the heights attained by the two balls respectively is . The
x
value of x is __________. [JEE Adv, 2022]
PW Web/App - https://smart.link/7wwosivoicgd4
Library- https://smart.link/sdfez8ejd80if
