Sample questions for second test

Here are a few questions to ponder:

1) You're standing 10 m from the bottom of a building. Your friend stands at her open window, 15 meters above you. You have a T-shirt launcher, which you know can launch a T-shirt 25 meters straight up. Can you launch a T-shirt to your friend, so that she can catch it? If so, at what angle should you aim the launcher?

2) A chunk of ice on the roof breaks loose, slides down the roof, and lands on the ground. If the ice was initially 3 m from the edge of the roof, that edge is 6 m above the ground, and the roof is pitched at 40 degrees, how far from the house does the chunk of ice land?

3)   You intend to attach a rock to a rope, and then to swing the rock in a vertical circle. You want the rope never to go slack, so you realize there's some minimum speed at which the rock must be moving, for a given length of rope. You also realize that the tension in the rope will likely be at times greater than the weight of the rock. If your rope can handle a tension of 100 pounds without breaking, what is the heaviest rock you can swing on this rope? Does the length of  the rope affect your answer?

4)  Suzy (30 kg) rides her 9 kg tricycle at 1.5 m/s. Joey (25 kg) chases her and hops onto the back of the tricycle. If Joey is running at 2.0 m/s when he hops on, how fast is the trike going just after Joey has jumped on?

5) Hey, remember the monkey question? We have a monkey of mass m, and a bunch of bananas also of mass m. The bananas are at one end of a rope, which passes over a frictionless pulley or two at the ceiling. The monkey is climbing (up or down) the other side of the rope, and at the outset he is about 10 feet below the bananas. Up near the ceiling is a group of ravenous gorillas, who will happily eat bananas and monkeys. Down on the floor is another group of similarly inclined gorillas. Face it, the monkey cannot escape death. However, he would like a last meal of tasty bananas. Can he get to the bananas, by climbing up or down the rope, before the gorillas get them or him?

6)  We hang two springs of identical length but different spring constants side by side, and then attach a 2 kg mass to the bottom ends of both springs. Spring 1 has a spring constant of 200 N/m and spring 2 has a spring constant of 300 N/m. We gently lower the mass to its equilibrium position. By how much is each spring stretched? We then pull the mass down by three centimeters. What is the greatest height it achieves after we let it go? What is the greatest speed it achieves after we let it go? The mass would undergo the same motions if we replaced these two springs with one spring; what is the spring constant of that replacement spring?

Quick answers are down below:

Answers:

(3) 16.7 pounds

(4)  1.7 m/s

(5) No

(6) 3 cm above the equilibrium position; 0.47 m/s; 500 N/m