1) A 10 kg rocket is placed on a launch pad that is 100 meters above perfectly flat terrain. The rockets ignition system gives it a force of 1000 N at a 30 angle to the horizontal. After 5 seconds, the rocket runs out of fuel. Ignore any air drag and ignore the change in mass caused by burning the fuel. A) Draw the FBD before and after the rocket runs out of fuel. B) How high above the ground does the rocket get? C) How far has the rocket traveled in the x direction when it reaches the peak of its path? D) How far does the rocket travel in the x direction before it hits the ground? E) How long is the rocket in the air? F) What is the velocity vector when the rocket hits the ground? The scalar value of velocity?

2) Theres a ride at the amusement park called the Spinning Terror. Its a large cylinder with a

diameter of 20 m thats raised into the air and spun so fast that everyone is pinned against the wall so that the floor can be dropped away. Assuming that the coefficient of static friction between the wall and any object is 0.25, what is the minimum velocity that the Spinning Terror must spin at such that no one will fall out of the ride?

3) An empty cart with mass 50 kg is connected by a rope through a pulley to a wall. The cart is initially at rest on a ramp. The ramp forms a 30 angle with the horizontal and has coefficients of friction equal to 0.2 and 0.1. The cart is 50 meters above the ground vertically. The rope that connects the cart with the wall is rated to a maximum tensional force of 1000 N.

A) How much additional weight can be loaded onto the cart before the rope snaps? B) Assume that 50 kg is added to the cart and then the rope is cut. What is the carts

acceleration? How fast is the cart moving at the bottom of the ramp? How long does it take the cart to reach the bottom of the ramp?

C) Assume the facts from part B still apply. Now the ramp is traveling on a flat frictionless surface. What is the carts velocity after a 10 kg rock drops from the sky and lands perfectly vertically into the cart?

D) Assume the facts from part C still apply. Now the cart and the rock crash and latch onto an empty cart with mass 50 kg that was initially at rest. What is the carts velocity after the collision?

E) Assume the facts from part D still apply. A gunman tries to stop the combined carts by shooting a bullet into the carts such that the bullet does not pass through the carts. Assume the bullet travels perfectly horizontally in the opposite direction of the combined carts and weighs 10 g. How fast does the bullet have to be moving in order to stop the cart?

4) A 50 kg rocket is launched into the air from the ground at an initial velocity of 50*sqrt(2) m/s. The launch path forms a 45 angle with the ground. At the peak of its path, the rocket blows up into two pieces, one with mass 10 kg and the other with mass 40 kg. After the explosion, the 10 kg piece falls straight down and hits the ground in 3 seconds. A) How long does it take for the 40 kg piece to hit the ground? B) How far did the 40 kg piece travel in the horizontal direction?

5) A window cleaner and his platform have a total mass of 170 kg. The platform is suspended from

a pulley by a counterweight of 100 kg.

A) How much force should the window cleaner apply to the rope so he can raise himself at

constant speed? B) Suppose the window cleaner is ascending at constant speed of 0.3 m/s towards a window 5

meters above him. What force should he apply so that he stops just in front of the window?

6) A highway on-ramp is banked at an angle and has a radius R.

A) Derive the ideal speed the on-ramp.

B) Given the coefficient of friction , what is the maximum speed a car can go on the on-ramp and avoid spinning out?

C) What is the minimum speed a car can go without sliding down the ramp?