Concept explainers
a.
To write a set of parametric equations that model the path of the baseball.
a.
Answer to Problem 63E
Explanation of Solution
Given: The ball is hit at a point 3 ft above the ground at an angle
Calculation:
The velocity of the ball in feet per second can be given as
Therefore, the parametric equations for the path of the ball can be given as:
That is,
b.
To graph the path of the ball when
b.
Explanation of Solution
Given:
Graph:
The parametric equation for
Now, graph these parametric equations using graphing utility as shown below.
From the graph it can be seen that the ball hits the ground at a distance of around 350 ft. So, it is not a home run.
c.
To graph the path of the ball when
c.
Explanation of Solution
Given:
Graph:
The parametric equation for
Now, graph these parametric equations using graphing utility as shown below.
From the graph it can be seen that the ball hits the ground at a distance of around 490 ft. The height of the ball at a distance of 408 ft is around 13 ft. So, it is a home run.
d.
To find the minimum value of the angle
d.
Answer to Problem 63E
Explanation of Solution
Given: The parametric equations
Calculation:
The home will be hit if
Now,
And,
Now, find the solutions of this inequality, graph the equations
From the graph it can observed that the equation
So, the minimum angle required to hit a home run is
Chapter 9 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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