Saturday, November 20, 2010

Free fall

A. Drop /Throw Down Problems

1. A peso is dropped into a well and it falls for 3 seconds before hitting the water. What is the peso's average speed during its 3 second drop?

2. A rock is dropped from the top of an overhang and strikes the ground 6.5 seconds later. How high is the overhang in meters?

3. It takes 0.210s for a dropped wrench to travel past a poster that is 1.35 meters tall. How high above the top of the poster was the wrench released?

4. A falling paratrooper (100 kg with parachute) experiences air resistance equal to 25% of his weight. What is his acceleration?

5. Consider a transparent elevator accelerating upward with acceleration equal to that of the gravity. If a rock was dropped inside the elevator, what would an observer on the ground see the rock do?

B. Throw Up Problems

1. You throw a ball downward from a window at a speed of 2.0 m/s. The ball accelerates at 9.8 m/s2.
a. How fast is it moving when it hits the sidewalk 2.5 m below?
b. If you throw the same ball up instead of down, how fast is it moving when it hits the sidewalk?

2. A ball is thrown straight up with a speed of 4.6 m/s. How long does the ball take to reach its maximum height?

3. A round is launched straight up at 460 m/s. How long will it take it to reach its apex and how high will that be? (air resistance may be neglected.)

4. What height will a dart achieve 7 seconds after being blown straight up at 50 m/s?

5. An apple thrown straight upward rises to 24 m above its launch point. At what height has apple's speed decreased to one-half of its initial value?

6. A stone is flung straight up from a point 1.50 m above the ground and with an initial speed of 19.6 m/s.
a. What is the stone's maximum height above the ground?
b. How much time passes before the stone hits the ground?

7. A blimp is hovering above the ground. When the pilot drops a sandbag overboard, the blimp rises with a constant velocity of 2 m/s. At the moment the sandbag hits the ground, the blimp is 50 m above the ground.
a. How far above the ground was the blimp when the sandbag was dropped?
b. When the sandbag is halfway to the ground, what is its acceleration?

8. A helicopter is ascending vertically with a speed of 5.00 m/s. At a height of 105 m above the ground, a package is dropped from a window. How much time does it take for the package to reach the ground?

9. A rock is thrown up at an initial velocity of 9.8 m/s. What is the time it takes to hit the ground?

C. Catch Up Problems

1. An archer shoots an arrow with an initial velocity of 21 m/s straight up from his bow. He quickly reloads and shoots another arrow in the same way 3.0 s later. At what time and height do the arrows meet?

2. A hoist is lifting a naturalist to the top of a cliff at 2.03 m/s vertically. The naturalist suddenly realizes she has left her pet rock behind. A friend picks it up and tosses it straight upward. If the naturalist is 2.50 m above her friend, what is the minimum initial speed the pet rock must have to reach the naturalist?

3. A boy shoots a rock from his slingshot at a target just as the target drops from a tree branch. Should the boy aim a little above the target, a little below the target, or straight at the target?