(a)
The velocity of the lighter ball before impact.
(a)
Answer to Problem 76GP
The velocity of the lighter ball before impact is
Explanation of Solution
Given:
The mass of the ball A is
The mass of the ball B is
The angle is
Formula used:
The expression for velocity is,
Here, g is the acceleration due to gravity and h is the height.
Calculation:
Consider the acceleration due to gravity as
Sketch the representation of balls as shown below.
The height h is,
The velocity of the lighter ball before impact is,
Conclusion:
Thus, the velocity of the lighter ball before impact is
(b)
The velocity of each ball after the elastic collision.
(b)
Answer to Problem 76GP
The velocity of ball A after the elastic collision is
The velocity of ball B after the elastic collision is
Explanation of Solution
Given:
The mass of the ball A is
The mass of the ball B is
The angle is
Formula used:
The expression for relative velocity is,
Here,
The expression for law of conservation of momentum is,
Here,
Calculation:
From part (a), the velocity of the lighter ball before impact is
The relative velocity is,
The speed of each object using the relation of conservation of momentum is,
The speed of the ball A using equation (1) is,
Conclusion:
Thus, the velocity of ball A after the elastic collision is
(c)
The maximum height of each ball after elastic collision.
(c)
Answer to Problem 76GP
The maximum height of ball A after elastic collision is
The maximum height of ball B after elastic collision is
Explanation of Solution
Given:
The mass of the meteor is
The mass of the Earth is
The speed of meteor is
Formula used:
The expression for the height is,
Here, v is the velocity and g is the acceleration due to gravity.
Calculation:
Consider the acceleration due to gravity as
From part (b), the velocity of ball A after the elastic collision is
The velocity of ball B after the elastic collision is
The height of the ball A is,
The height of the ball A is,
Conclusion:
Thus, the maximum height of ball A after elastic collision is
Chapter 7 Solutions
Physics: Principles with Applications
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