Final answer:
1. The pencil that rolls off the table will hit faster. 2. Throwing the balloon downwards increases its overall velocity and therefore, the speed at which it hits the ground. 3. Batman should NOT let go of the building and hope to dodge the bullet by falling downward.
Step-by-step explanation:
1. Which will hit the ground FASTER (greater ), a pencil that is dropped from the top of the table ( = 0) or a pencil that rolls of the edge of the table ( > 0)? (Assume the table is level and both pencils leave the table at the same instant.)
The pencil that rolls off the table will hit faster. This is because it has an initial horizontal velocity, which increases its overall speed of descent compared to the pencil that is simply dropped.
2. You are throwing a water balloon as hard as you can off the top of the bleachers. You want the balloon to hit the ground with as great a velocity as possible. Which of these actions will help the hit the ground fastest—that is, with greatest ?
Throwing the balloon DOWN at the opposite angle (-θ) with the same initial velocity vmax. This is because throwing the balloon downwards increases its overall velocity and therefore, the speed at which it hits the ground.
3. Batman, hanging from the top of a low building, sees a criminal a long-distance away pointing a gun over his head at him. (The gun has no sighting tool, and the criminal does not know physics.) Assume Batman reacts just as the criminal fires the gun.
Batman should NOT let go of the building and hope to dodge the bullet by falling downward. This is because the bullet will travel faster than Batman can fall, so he would be unable to dodge it by falling.