Question

1. how much force is needed to move a 0.1 kg snowball at a rate of 15 m/s² upward?
2. a 0.02 n push accelerates a table - tennis ball along a table at 8 m/s² north. what is the mass of the ball?
3. at lift - off, an astronaut on the space shuttle experiences an acceleration of approxi - mately 35 m/s² upward. what force does an 80 kg astronaut experience during this acceleration?
4. what is the acceleration of a train with a mass of 3.2×10⁷ kg that pushes itself for - ward with 2.4×10¹⁰ n of force?

part 3: the force of gravity
forces are not always exerted on objects by direct physical contact, such as a hand push - ing a door closed. for instance, the earth exerts the force of gravity on objects even when the objects are not directly touching the ground. the acceleration on an object due to the force of gravity is 9.8 m/s² downward. in other words, for every second an ob - ject is falling, its velocity increases by 9.8 m/s downward.

1. a. a 9 kg bowling ball rolls off a table and strikes the ground. if the ball is in the air for 0.5 seconds, how fast is the ball moving when it hits the ground?

b. another bowling ball with one - fifth less mass rolls off the same table and strikes the ground. when this ball hits the ground, is it moving faster, slower, or the same speed as the first ball? explain your answer.

Explanation:

Step1: Use the formula \(v = v_0+at\)

Since the ball rolls off the table (initial vertical velocity \(v_0 = 0\) m/s), \(a = g=9.8\) m/s² (acceleration due to gravity), and \(t = 0.5\) s.

Step2: Substitute the values into the formula

\(v=0 + 9.8\times0.5\)
\(v = 4.9\) m/s

The acceleration due to gravity \(g = 9.8\) m/s² acts on all objects near the Earth's surface, regardless of their mass. The formula for final velocity \(v=v_0 + at\) (where \(v_0 = 0\) for a ball rolling off a table horizontally, \(a = g\), and \(t\) is the time of fall) shows that mass does not affect the final velocity in free - fall (neglecting air resistance).

Answer:

The ball is moving at \(4.9\) m/s when it hits the ground.