Question

1. if you are driving at 10 m/s and throw a ball forward at 5 m/s.

a. what is the speed of the ball, relative to the ground?

b. what would its speed be if you threw it backwards instead, relative to the ground?

c. what would its speed be if you threw it backwards instead, relative to the car?

unit 2

1. identify how an objects inertia changes in each of the following situations:

a. its mass is cut in half

b. its velocity is doubled

c. its acceleration decreases by 25%

Explanation:

Question 21

Part a

Step1: Understand relative velocity

The car's speed is \( 10 \, \text{m/s} \) and the ball is thrown forward at \( 5 \, \text{m/s} \) relative to the car. To find the speed relative to the ground, we add the two speeds (since they are in the same direction).
\[
v_{\text{ground}} = v_{\text{car}} + v_{\text{ball relative to car}}
\]

Step2: Substitute values

Substitute \( v_{\text{car}} = 10 \, \text{m/s} \) and \( v_{\text{ball relative to car}} = 5 \, \text{m/s} \) into the formula.
\[
v_{\text{ground}} = 10 + 5 = 15 \, \text{m/s}
\]

Step1: Understand relative velocity (opposite direction)

The car's speed is \( 10 \, \text{m/s} \) and the ball is thrown backward at \( 5 \, \text{m/s} \) relative to the car. To find the speed relative to the ground, we subtract the ball's speed (relative to car) from the car's speed (since they are in opposite directions).
\[
v_{\text{ground}} = v_{\text{car}} - v_{\text{ball relative to car}}
\]

Step2: Substitute values

Substitute \( v_{\text{car}} = 10 \, \text{m/s} \) and \( v_{\text{ball relative to car}} = 5 \, \text{m/s} \) into the formula.
\[
v_{\text{ground}} = 10 - 5 = 5 \, \text{m/s}
\]

Step1: Relative velocity to the car

The speed of the ball relative to the car is the speed at which it is thrown relative to the car. Since it is thrown backward at \( 5 \, \text{m/s} \) relative to the car, its speed relative to the car is \( 5 \, \text{m/s} \) (the direction is backward, but the question asks for speed, which is a scalar, so we consider the magnitude).

Answer:

\( 15 \, \text{m/s} \)

Part b