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[Use the gravitational acceleration 𝑔𝑔 as 9.8 m/s2 throughout the problems.]
At a stop light, a truck traveling at 16 m/s passes a car as it starts from rest. The truck
travels at constant velocity and the car accelerates at 2 m/s2. How much time does the car
take to catch up to the truck? (5 pt)
Two vectors lie with their tails at the same point. When the angle between them is increased
by 30°, the magnitude of their vector product becomes √3 times larger. What was the
original angle between them? (10 pt)
A ball is thrown horizontally from the top of a 500-m high hill. It strikes the ground at an
angle of 45°. With what speed was it thrown? (5 pt)
A 1000-kg elevator is rising and its speed is increasing at 3 m/s2. What is the tension in the
elevator cable? (5 pt)
A steel ball is dropped from a building’s roof and passes a window, taking 0.5 s to fall from
the top to the bottom of the window, a distance of 4.9 m. It then falls to the ground. The
time the ball spends below the bottom of the window is 1.125 s. How tall is the building?
(15 pt)
If 2π‘Žπ‘Žβƒ— + 3𝑏𝑏�⃗ = 𝑐𝑐⃗, π‘Žπ‘Žβƒ— + 2𝑏𝑏�⃗ = 3𝑐𝑐⃗, and 𝑐𝑐⃗ = 3iΜ‚ + 2jΜ‚, then what are π‘Žπ‘Žβƒ— and 𝑏𝑏�⃗? (10 pt)
In a soccer match, a player A is running due north toward the goal with a speed of 8 m/s
relative to the ground. Other player B passes the ball to him. The ball has a speed of 12 m/s
and is moving in a direction 45° east of north, relative to the ground. What are the
magnitude and direction of the ball’s velocity relative to the player A? (5 pt)
A soccer kicker gives the ball an initial speed of 25 m/s with the elevation angle of 30°. If
the ball hits the upper horizontal goalposts bar that is 3.44 m above the ground, find his
kicking positions i.e. the ground distance from the goalposts. Ignore the air friction. (15 pt)
An interstellar ship has a mass of 1.2×106 kg and is initially at rest relative to a star system.
(a) What constant acceleration is needed to bring the ship up to a speed of 0.10𝑐𝑐 (where 𝑐𝑐
is the speed of light, 3.0×108 m/s) relative to the star system in 3.0 days? (b) What is that
acceleration in 𝑔𝑔 units? (c) What force is required for the acceleration? (d) If the engines
are shut down when 0.10𝑐𝑐 is reached (the speed then remains constant), how long does the
ship take (start to finish) to journey 5.0 light-months, the distance that light travels in 5.0
months? (15 pt)
10. A 5.00-kg box that is several hundred meters above the surface of the earth is suspended
from the end of a short vertical rope of negligible mass. A time-dependent upward force is
applied to the upper end of the rope, and this results in a tension in the rope of 𝑇𝑇(𝑑𝑑) = 𝑏𝑏𝑏𝑏
with 𝑏𝑏 = 49 N/s. The box is at rest at 𝑑𝑑 = 0. The only forces on the box are the tension in
the rope and gravity. (a) What is the velocity of the box at 𝑑𝑑 =1 s? (b) What is the
maximum distance that the box reaches below its initial position? (c) At what value of 𝑑𝑑
does the box return to its initial position? (15 pt)