(a)
The initial velocity that must be imparted to the golf ball so that it crosses over a tree and lands on the green.
(a)
Answer to Problem 43P
The initial velocity of the golf ball is found to have a magnitude
Explanation of Solution
Given:
Horizontal distance to the tree,
Height of the tree,
The golf ball just grazes over the top of the tree, hence its maximum height in its trajectory is equal to the height of the tree.
Formula used:
For the vertical motion of the ball,
Here,
The horizontal motion of the ball is uniform, since no force acts along the horizontal direction.
For horizontal motion
Here,
The magnitude of the velocity of projection is given by,
The angle of projection is given by
Calculation:
The tree is at the topmost point of the ball’s trajectory. At this point, the vertical component of its velocity becomes equal to zero.
Substitute
Calculate the time taken to reach the height t using equation (2) and substituting
In the time t the ball travels a horizontal distance x . Substitute
Use the calculated values of
Conclusion:
Thus the initial velocity that must be imparted to the golf ball so that it crosses over a tree and lands on the green is found to have magnitude
(b)
The horizontal distance the ball travels after crossing the tree before hitting the ground.
(b)
Answer to Problem 43P
The horizontal distance the ball travels after crossing the tree before hitting the ground is found to be
Explanation of Solution
Given:
The vertical height of the ground from the point of launch,
The vertical component of the ball’s initial velocity,
The horizontal component of the ball’s initial velocity,
Time taken by the ball to cross the tree,
Formula used:
If the time of flight of the ball is
The time taken to travel the distance d after crossing the tree is given by
The horizontal distance d is given by
Calculation:
Substitute the given values of variables in equation (6) to calculate the value of
Simplify the equation:
Solve the quadratic to obtain the values of
Since, it is required to find the time taken to reach the green,
Calculate the value of
Calculate the distance d using equation (8).
Conclusion:
Thus, the horizontal distance the ball travels after crossing the tree before hitting the ground is found to be
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- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning