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 +9.0 m/s at an angle of 35.0° find the following: a) How long will each stone be in the air assuming the stones land at the same level as they are launched? Show all work.

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

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

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

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.