Assume g = 9.80 m/s2

? 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: ? What are the velocities in the X and Y directions? Show all work.

? How long will each stone be in the air? Show all work.

? What is the range (horizontal distance) that the stone will travel? Show all work

? What is the maximum height of the launched stones? Show all work.

? What is the velocity of each stone as it hits the ground?

(8 points) ? 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. ? Find the magnitude and direction of the centripetal acceleration when he is spinning at constant angular velocity.

? Find the magnitude and direction of the centripetal force when he is spinning at constant angular velocity.

? How many g's is the astronaut experiencing when moving at constant angular velocity?

? 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) ? 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.

TranscribedText

Angular displacement L Angular Displacement of a Pendulum 0.060 0.040 0.020 0.000 0.020 -0.040 -0.060 MMW 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time (s)