1. A box is dropped from the roof of a 30m building. As it falls, it passes a window that is 2 meters high and whose base is located 10 meters above street level. Determine the time required for the box to move past the window. In other words, how long is the box in the field of vision of a person looking out the window? Neglect air resistance. 2. An object is moving in one-dimension with a velocity of 0.5t+2.5sin(21) m/s. It starts from rest at x-0. Determine its position and acceleration at t-3 seconds. 3. The disc (m-2 kg, r-10 cm) shown below is attached to a motor. It is rotating counterclockwise at a constant angular speed of 30 rpm. When the power is cut off it slows with a constant angular deceleration of 1 rad/s. (a) Calculate the net torque acting on the disc. (b) What is the initial angular velocity (in rad/s)? Don't forget the direction. (c) Find the initial velocity (magnitude and direction) of point P. (d) When the angular speed has slowed to half of its initial value, determine the magnitude and direction of total acceleration of point P. Use a unit vector and an angle to find specify direction. Hint: Find the tangential and centripetal accelerations and combine them. (e) How long does it take to come to rest? (f) What is the final location of point P? Give your answer in degrees with 0 denoting the positive x-direction. 4. A student sits on a stool that is free to rotate about a vertical axis. He holds his arms extended horizontally with a 35.6 N weight in each hand. The instructor sets him rotating with an angular speed of 0.5 rev/s. Assume that friction is negligible. The rotational inertia of the student remains approximately constant at 5.4 kg-m as he pulls his hands to his sides so that any change is due to only to the pulling the weights in. Take the original distance of the weights from the axis of rotation to be 0.91 m and their final distance 0.15 m. Find the final angular velocity of the student. 5. A railroad flatcar of weight W can roll without friction along a straight horizontal track as shown below. Initially a man of weight w is standing on the car which is moving to the right with speed v.. What is the change in velocity of the car is the man runs to the left so that his speed relative to the car is vel just before jumping off the left end? GOLD W 6. Two flywheels are connected by a non-slipping belt as shown in the accompanying figure: 1,-4 kg m, r,-0.2 m, 1-20 kg-m, r-0.3 m. If a torque of 10 N-m is applied to the smaller flywheel, what are the angular accelerations of the two flywheels? 52 7. A cylinder of length L and radius r has a mass m. Two cords are wrapped around the cylinder, one near each end, and the cord ends are attached to hooks on the ceiling. The cylinder is held horizontally with the two cords exactly and is then released. Find the tension in each of the cords as they unwind and the acceleration with which the cylinder falls.