Question

a pitching machine is programmed to pitch baseballs horizontally at a speed of 87 mph. the machine is mounted on a truck and aimed forward. as the truck drives toward a man at a speed of 65 mph, the machine shoots a ball towards him. determine the correct relative speed for each object pair. the speed of the pitching machine relative to the truck; the speed of the pitched ball relative to the truck; the speed of the pitching machine relative to the man; the speed of the pitched ball relative to the man.

Explanation:

Step1: Pitching machine relative to truck

The pitching machine is mounted on the truck, so their relative speed is \( 0 \) mph (since they move together with the same velocity relative to each other).

Step2: Pitched ball relative to truck

The ball is pitched horizontally at \( 87 \) mph relative to the machine, and the machine is on the truck. So the speed of the ball relative to the truck is \( 87 \) mph (as the machine's motion relative to the truck is zero, the ball's speed relative to the truck is its speed relative to the machine).

Step3: Pitching machine relative to man

The truck (with the machine) is moving toward the man at \( 65 \) mph. So the speed of the machine relative to the man is \( 65 \) mph (since the machine is on the truck moving at \( 65 \) mph toward the man).

Step4: Pitched ball relative to man

The ball's speed relative to the truck is \( 87 \) mph, and the truck's speed relative to the man is \( 65 \) mph (both toward the man). So we add these speeds: \( 87 + 65 = 152 \) mph.

Answer:

• The speed of the pitching machine relative to the truck: \( 0 \) mph
• The speed of the pitched ball relative to the truck: \( 87 \) mph
• The speed of the pitching machine relative to the man: \( 65 \) mph
• The speed of the pitched ball relative to the man: \( 152 \) mph