Concept explainers
(a)
The distance where the ball hits the ground.
(a)
Explanation of Solution
Given: The distance between the woman and the wall is
The velocity of the ball is
The ball is at the distance of
The angle made by the ball with the horizontal is
Formula used:
The diagram represents the path followed by the ball.
Write the expression for the distance at which the ball hits.
Here
Write the expression for the vertical displacement of the ball.
Here
The vertical component of velocity is:
Substitute
Write the expression for the horizontal distance ball.
Here,
Calculation:
Substitute
Solve the above quadratic equation for
Substitute
Substitute
Conclusion:
Thus, the ball hits the ground at
(b)
The time for which the ball is in the air.
(b)
Explanation of Solution
Given:
The distance between the woman and the wall is
The velocity of the ball is
The ball is at the distance of
The angle made by the ball with the horizontal is
Formula used:
Write the expression for the time.
Here,
Substitute
Calculation:
Substitute
for
Conclusion:
Thus, the ball is in the air for
(c)
The distance at which the ball hits the ground.
(c)
Explanation of Solution
Given:
The distance between the woman and the wall is
The velocity of the ball is
The ball is at the distance of
The angle made by the ball with the horizontal is
Formula used:
Write the expression for the relation between initial and final velocity in the vertical direction.
Substitute
Write the expression to represent the vertical direction.
Substitute
Calculation:
Substitute
Substitute
Conclusion:
Thus, the distance at which the ball hits the ground is
(d)
The time for which the ball was in the air after it hit the wall.
(d)
Explanation of Solution
Given:
The distance between the woman and the wall is
The velocity of the ball is
The ball is at the distance of
The angle made by the ball with the horizontal is
Formula used:
Write the expression to represent the vertical direction.
Here,
Substitute
When the ball hits the ground, the vertical distance becomes zero.
Calculation:
Substitute
Solve the quadratic equation for
Conclusion:
Thus, the time for which the ball was in the air after it hit the wall is
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Chapter 3 Solutions
Physics for Scientists and Engineers
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