1. You may solve one of the two subquestions here and circle the subquestion for which to be graded. Subquestion (a) will be graded if no explicit selection is made.
(a) A ball is thrown vertically upward from the edge of a tower that is 50.0m above the ground. The ball is thrown with an initial speed of 30.0m/s. It returns just missing the tower, and finally hits the ground. Ignore the air resistance. i. Find the time required for the ball to reach its maximum height. ii. What is the highest distance of the ball above the ground? (10 points)
(b) A student wants to throw a stone into a window h = 7m high and x = 16m away from him. He throws the stone along 36.9^o above the horizontal and the stone just hits the window. Find the initial velocity of the stone and the time the stone takes to hit the window.
(10/15 points)

2. Two blocks A, B of mass m = 1kg are connected by a cord through a frictionless pulley. Block A rests on an incline which is inclined at an angle 36.9^o above the horizontal and block B hangs in the air h = 1m above the ground. Assume the coefficient of kinetic friction between the block and the incline is 0.2. The blocks are released from rest.
(a) Draw the free body diagram for the two blocks.
(b) Use the second law of Newton to find the velocity of block B when it hits the ground.
(c) Resolve (b) by work-energy theorem.
(25 points)

3. You may solve one of the two subquestions here and circle the subquestion for which to be graded. Subquestion (a) will be graded if no explicit selection is made.
(a) A m = 2000kg limousine is traveling at a speed of v_m = 20.0m/s to the north on a through street when it is struck by a M = 3000kg panel truck traveling to the east at v_M = 10.0m/s. The vehicles lock together and leave the point of impact at an angle of 53.1^o north of east with velocity v'. The coefficient of kinetic friction between cars and ground is 0.5. i. It is a good approximation that linear momentum is conserved during the impact. Please explain. ii. Determine the velocity v' with which the cars leave the point of impact. iii. Find the slippage of the cars after the impact. (25 points)
(b) A diver comes off a diving board with arms straight up and legs straight down, giving him a moment of inertia about his axis of rotation equal to 20kgm². He then tucks into a small ball, decreasing his moment of inertia to 3.6kgm². While tucked he makes two complete revolutions in 1.2s. If he hadn’t tucked at all, how many revolutions would he have made in the 1.5s from board to water? You can make reasonable approximations. (25 points)

(25 points)

4. A block of mass 10kg connected to a massless spring undergoes simple harmonic motion (SHM) on a horizontal frictionless surface. At t = 0 the block is released from rest at x₀ = -0.5m, and it reaches its maximum speed v_max for the first time at x = 0 and t = s.
(a) Find the period T , the amplitude A, angular velocity and phase angle of this SHM and then write down x(t), the position of the block at any time.
(b) Find the force constant of the spring.
(c) Find v_max.
(d) (Optional) Find the shortest time that it takes for the block to travel to x = 0.8A.
(20/30 points)

5. You may solve one of the two subquestions here and circle the subquestion for which to be graded. Subquestion (a) will be graded if no explicit selection is made.
(a) Tom wants to float himself in water using a plastic board. His weight is 75kg. Find the minimum size of the board he needs. The thickness of the plastic board is 2cm and its density 0.2g/cm³. The density of a person is 1.2 × 10³kg/m³. You can assume Tom is totally submerged in water.
(b) Venturi meter can be used to measure flow speed in a pipe. If the cross section areas A₁ = 4cm² and A ₂ = 2cm² at the throat, the difference in height of the liquid levels in the two vertical tubes is h = 3cm. Find the flow speed at cross area A₁.
(20/25 points)

6. To cool a cup of water at 27^oC, a block of ice is put into the cup. Assume the cup is made of glass and its mass is m_glass = 50g, the amount of the water is m_water = 200g, and the volume of the ice block is V _ice = 10cm³. You may use the specific heat capacity of glass c_glass = 838J/kgK, the specific heat capacity of water c_water = 4190J/kgK, the fusion heat of water L_f = 334 × 10³J/kg, and the density of ice 0.92 × 10³kg/m³.
(a) Find the mass of the ice.
(b) Find the final temperature of the water. Ignore the heat exchange with the environment.
(20 points)

7. You need not show any calculation for the following subquestions.
(a) Explain the origin of g = 9.8m/s².
(b) Provide one example in your everyday life which may be explained by what you have learned in the course and explain it.
(c) How do you think about this course? Write a short paragraph within 150 words.
(25 points)