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Q. 59

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 157

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Short Answer

A ball is shot from a compressed-air gun at twice its terminal speed.

a. What is the ball's initial acceleration, as a multiple of , if it is shot straight up?

b. What is the ball's initial acceleration, as a multiple of , if it is shot straight down?

Part(a): Balls initial acceleration is

Part (b): Balls initial acceleration is .

See the step by step solution

Step by Step Solution

Part (a) Step 1: Given

Balls speed is twice its initial speed:

Ball is shot up.

Part(a) Step 2: Formula used.

part (a) Step 3: Calculation.

The formula for the drag force is given as:

Where, is ball's speed

And is terminal speed.

When the ball is shot with twice of its terminal speed, forces acting simultaneously on it.

1. (drag force opposite in the direction of motion)

2. (Earth's gravitational pull always in downward direction)

So, the net force on the ball in the vertical direction can be given as

Speed of the ball = twice the terminal speed of the ball

So,

So, the Ball's initial acceleration, if it is shot straight up is .

Part (b) Step 4: Given

Balls speed is twice its initial speed:

Ball is shot up.

Part (b) Step 5: Formula used.

Part (b) Step 6: Calculation.

The formula for the drag force is given as

Where, is ball's speed

And, is terminal speed.

When the ball is shot with twice of its terminal speed, 2 forces acting simultaneously on it.

1. (drag force opposite in the direction of motion)

2. (Earth's gravitational pull always in downward direction)

So, the net force on the ball in vertical direction can be given as:

Part (b) Step 7: Calculations

Speed of the ball twice the terminal speed of the ball

So,

So, the Ball's initial acceleration, if it is shot straight up is .

Step 8: Conclusion

Part (a): The Ball's initial acceleration, if it is shot straight up is

Part (b): The Ball's initial acceleration, if it is shot straight up is

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