University Physics I (Spring 2021)
Final Exam
Write down your answers to the problems (8 in total) on the separate answer sheet,
together with your name and student ID.
1.(15 points) A projectile is shot from the edge of a cliff h=56 m above the ground level with an initial
speed v0=10 m/s at an angle of 370 with the horizontal, as shown in Fig.1.
(a). Determine the time taken by the projectile to hit the point P at ground level.
(b). Determine the horizontal displacement X of the projectile as measured from the base of the cliff.
(c). Determine the horizontal and vertical components of its velocity at the instant of hitting point P.
[hint: use sin370=0.6, cos370=0.8, and gravitational acceleration g=10 m/s2.]
Fig.1 for Problem 1
, 2. (15 points) An incline that makes an angle 37 with the horizontal is fixed on the ground. A
block of mass mA rests on the incline's surface whose kinetic friction coefficient is k 0.5 (assume
the static friction coefficient is roughly of the same value). This block is connected by a very light cord,
which passes over a massless and frictionless pulley, to a second block of mass mB=5.0kg, which hangs
freely and vertically as shown in Fig.2. Now the system is released from rest.
(a). If mA =3.0kg, the block A will be sliding down or up the incline? What is the acceleration of the
system?
(b). If mA =35.0kg, the block A will be sliding down or up the incline? Determine the acceleration of the
system again. [hint: use sin370=0.6, cos370=0.8, and gravitational acceleration g=10 m/s2.]
Fig.2 for Problem 2
3. (10 points) A small ball of mass m, suspended by a cord of length L, revolves in a circle of radius
r L sin , where is the angle that the string makes with the vertical, see Fig.3.
(a). Determine the centripetal acceleration of the ball in terms of L, and gravitational acceleration g.
(b). Determine the speed v and the period T (time required for one full revolution) of the ball in terms of
L, and gravitational acceleration g.
Final Exam
Write down your answers to the problems (8 in total) on the separate answer sheet,
together with your name and student ID.
1.(15 points) A projectile is shot from the edge of a cliff h=56 m above the ground level with an initial
speed v0=10 m/s at an angle of 370 with the horizontal, as shown in Fig.1.
(a). Determine the time taken by the projectile to hit the point P at ground level.
(b). Determine the horizontal displacement X of the projectile as measured from the base of the cliff.
(c). Determine the horizontal and vertical components of its velocity at the instant of hitting point P.
[hint: use sin370=0.6, cos370=0.8, and gravitational acceleration g=10 m/s2.]
Fig.1 for Problem 1
, 2. (15 points) An incline that makes an angle 37 with the horizontal is fixed on the ground. A
block of mass mA rests on the incline's surface whose kinetic friction coefficient is k 0.5 (assume
the static friction coefficient is roughly of the same value). This block is connected by a very light cord,
which passes over a massless and frictionless pulley, to a second block of mass mB=5.0kg, which hangs
freely and vertically as shown in Fig.2. Now the system is released from rest.
(a). If mA =3.0kg, the block A will be sliding down or up the incline? What is the acceleration of the
system?
(b). If mA =35.0kg, the block A will be sliding down or up the incline? Determine the acceleration of the
system again. [hint: use sin370=0.6, cos370=0.8, and gravitational acceleration g=10 m/s2.]
Fig.2 for Problem 2
3. (10 points) A small ball of mass m, suspended by a cord of length L, revolves in a circle of radius
r L sin , where is the angle that the string makes with the vertical, see Fig.3.
(a). Determine the centripetal acceleration of the ball in terms of L, and gravitational acceleration g.
(b). Determine the speed v and the period T (time required for one full revolution) of the ball in terms of
L, and gravitational acceleration g.
