a.
To Graph: The parametric equations which represent the position of a fly ball and the fence at the boundary respectively for
To State: Whether the fly ball clears the fence.
The fly ball does not clear the fence.
Given: The parametric equations which represent the position of a fly ball and the fence at the boundary respectively:
The allowed values
Concepts Used:
The function call
The function call
For the fly ball to clear the fence, the graph of trajectory of ball must pass above the fence without touching it.
Graph:
Interpretation:
The trajectory of the fly ball has not passed completely above the fence. It hits the fence near its bottom. So, the fly ball does not clear the fence.
b.
To Graph: The parametric equations given in the previous part for the angle
To State: Whether the fly ball clears the fence.
The fly ball does not clear the fence.
Given: The parametric equations which represent the position of a fly ball and the fence at the boundary respectively:
The allowed values
Concepts Used:
The function call
The function call
For the fly ball to clear the fence, the graph of trajectory of ball must pass above the fence without touching it.
Graph:
Interpretation:
The trajectory of the fly ball has not passed completely above the fence. It hits the fence near its bottom. So, the fly ball does not clear the fence.
c.
To Determine: The optimal angle for hitting the ball.
To State: Whether the fly ball clears the fence.
The optimal angle is
Given: The parametric equations which represent the position of a fly ball and the fence at the boundary respectively:
The allowed values
Concepts Used:
The function call
The function call
For the fly ball to clear the fence, the graph of trajectory of ball must pass above the fence without touching it.
Graph:
By the process of hit and trial to plot the trajectory of the ball for various angles of hitting the ball, it was found that maximum distance was covered when the angle of hitting was
Interpretation:
The optimal angle is
Chapter 1 Solutions
EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
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