EP 105 General Physics I
First Midterm Exam FALL 2021
Date: 23/11/2021 Time: 17:00 Duration: 90 min.
Cheating is a serious offence and may lead to your dismissal from the university.
Write clearly your solutions steps to the answer book.
Solutions in the question paper will not be taken into account.
Constants: g = 9.8 m/s2, π = 3.14
QUESTION 1 (20 %)
Consider two vectors are defined as ⃗⃗ and ⃗⃗ . Determine,
a) the constant m that satisfies the cross product of two vectors is zero, and
b) the angle between two vectors.
SOLUTION
a)
⃗ ⃗⃗ | | ( ) ( ) ( )
( ) ( )
⃗⃗ ⃗⃗ ( )(
b) ⃗ ⃗⃗ ( ) ( ) ( (√ ) ( )
√ )
QUESTION 2 (20 %)
A stone is thrown vertically upward from a point near the top edge of a tall building. It just misses the edge on the
way down and passes a point 50 m below its starting point 5 s after it leaves the thrower's hand. Air resistance may
be ignored. a) What is the initial speed of the stone? b) How high does it rise above its starting point? c) What is the
magnitude of its velocity at the highest point?
SOLUTION
, QUESTION 3 (20 %)
A projectile is launched from the ground at an angle =45 to the horizontal and
initial speed v=21 m/s. At what height does the projectile hit a vertical wall that is
x=9.0 m away? (Neglect air resistance, sin45 = cos45 = 1/√ )
SOLUTION
QUESTION 4 (20 %)
A 55.0 kg crate pulled 11.0 m up a 44.0° ramp by a weightless string with a constant
tension 475 N. The coefficient of kinetic friction is 0.33 between the crate and the
surface. Calculate the work done by each force acting on the crate.
SOLUTION
First Midterm Exam FALL 2021
Date: 23/11/2021 Time: 17:00 Duration: 90 min.
Cheating is a serious offence and may lead to your dismissal from the university.
Write clearly your solutions steps to the answer book.
Solutions in the question paper will not be taken into account.
Constants: g = 9.8 m/s2, π = 3.14
QUESTION 1 (20 %)
Consider two vectors are defined as ⃗⃗ and ⃗⃗ . Determine,
a) the constant m that satisfies the cross product of two vectors is zero, and
b) the angle between two vectors.
SOLUTION
a)
⃗ ⃗⃗ | | ( ) ( ) ( )
( ) ( )
⃗⃗ ⃗⃗ ( )(
b) ⃗ ⃗⃗ ( ) ( ) ( (√ ) ( )
√ )
QUESTION 2 (20 %)
A stone is thrown vertically upward from a point near the top edge of a tall building. It just misses the edge on the
way down and passes a point 50 m below its starting point 5 s after it leaves the thrower's hand. Air resistance may
be ignored. a) What is the initial speed of the stone? b) How high does it rise above its starting point? c) What is the
magnitude of its velocity at the highest point?
SOLUTION
, QUESTION 3 (20 %)
A projectile is launched from the ground at an angle =45 to the horizontal and
initial speed v=21 m/s. At what height does the projectile hit a vertical wall that is
x=9.0 m away? (Neglect air resistance, sin45 = cos45 = 1/√ )
SOLUTION
QUESTION 4 (20 %)
A 55.0 kg crate pulled 11.0 m up a 44.0° ramp by a weightless string with a constant
tension 475 N. The coefficient of kinetic friction is 0.33 between the crate and the
surface. Calculate the work done by each force acting on the crate.
SOLUTION
