Concept explainers
(a)
The maximum when the ball has reached its first parabolic arc.
(a)
Explanation of Solution
Given:
The angle of ball above the horizontal is
The initial speed of the ball is
The increase in height is
Formula used:
Write the expression for the horizontal component of the ball.
Here,
Substitute
Write the expression for the vertical component of the ball.
Here,
Substitute
Write the equation for the
Substitute
When the ball is at the top of trajectory, the vertical velocity at this point is zero.
Substitute
Solve the above equation for
Substitute
Calculation:
Substitute
Conclusion:
The maximum height reached by the ball at its first parabolic arc is
(b)
The distance of the ball from the launch point to the ground for the first time.
(b)
Explanation of Solution
Given:
The angle of ball above the horizontal is
The initial speed of the ball is
The increase in height is
Formula used:
Write the expression for the range of the parabolic path.
Here,
Calculation:
Substitute
Conclusion:
The distance of the ball from the launch point to the ground for the first time is
(c)
The distance of the ball from the launch point to the ground for the second time.
(c)
Explanation of Solution
Given:
The angle of ball above the horizontal is
The initial speed of the ball is
The increase in height is
Formula used:
Write the expression for the total range of the ball.
Here,
Write the expression for the range of the parabolic path.
Here,
Write the expression for the resultant velocity.
Here,
Substitute
Write the expression for the relation between initial and final velocity.
Here,
Substitute
Substitute
Write the expression for the rebound angle
Substitute
Substitute
Write the expression for the
Calculation:
Substitute
Substitute
Conclusion:
The distance of the ball from the launch point to the ground for the second time is
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Chapter 3 Solutions
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