Assume g = 9.80 m/s²

(8 points)

1. During a medieval siege of a castle, the attacking army uses a trebuchet to hurl heavy stones at the castle walls. If the trebuchet launches the stones with a velocity of +40.0 m/s at an angle of 35.0 find the following:
2. What are the velocities in the X and Y directions? Show all work.
3. How long will each stone be in the air? Show all work.
4. What is the range (horizontal distance) that the stone will travel? Show all work
5. What is the maximum height of the launched stones? Show all work.
6. What is the velocity of each stone as it hits the ground?

(8 points)

1. A 85.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 20.0 m) and spun at a constant angular velocity of 15.0 rpm (revolutions per minute). He is then slowed and brought to a stop in 2.0 minutes.
2. Find the magnitude and direction of the centripetal acceleration when he is spinning at constant angular velocity.
3. Find the magnitude and direction of the centripetal force when he is spinning at constant angular velocity.
4. How many g's is the astronaut experiencing when moving at constant angular velocity?
5. Find the torque that is needed to bring the centrifuge to a stop knowing the centrifuge has a mass of 5500.0 kg (ignore all other forces) and the force is applied at the edge of the centrifuge (20.0 m radius). Hint: torque is based on the change of linear velocity.

Answer:

(9 points)

1. An astronaut lands on an alien planet. He places a pendulum (L = 0.200 m) on the surface and sets it in simple harmonic motion, as shown in this graph.