Analyzing the Motion of a Projectile A projectile is fired at an inclination of
Where
At what horizontal distance from the firing point is the height of the projectile
Find the maximum height of the projectile.
At what horizontal distance from the firing point will the projectile strike the ground?
Graph the function
Use a graphing utility to verify the results obtained in parts
When the height of the projectile is
(a)
To calculate: The horizontal distance from the firing point at which the height of the projectile is maximum.
Answer to Problem 74AYU
Solution:
The height of projectile is maximum at a distance
Explanation of Solution
Given Information:
A projectile is fired at an inclination of
Formula used:
The graph of the function
Calculation:
A projectile is fired at an inclination of
The graph of the function
Compare
The height of projectile is maximum at a distance
(b)
To calculate: The maximum height of the projectile, if the height
Answer to Problem 74AYU
Solution:
The maximum height of the projectile is
Explanation of Solution
Given Information:
A projectile is fired at an inclination of
Formula used:
The graph of the function
Calculation:
A projectile is fired at an inclination of
The graph of the function
Compare
The maximum height of projectile is
(c)
To calculate: The horizontal distance from the firing point at which the projectile will strike the ground, if the height
Answer to Problem 74AYU
Solution:
The projectile will strike the ground at
Explanation of Solution
Given Information:
A projectile is fired at an inclination of
Where
Formula used:
When the projectile touches the ground the height of the projectile becomes zero.
Calculation:
A projectile is fired at an inclination of
Where
When the projectile touches the ground the height of the projectile becomes zero.
The least common denominator is
Divide by
The equation
As
The projectile will strike the ground at
(d)
To graph: To graph
Explanation of Solution
Given Information:
Graph:
The equation of
To graph using graphing utility, follow the steps given below
Step 1: Press Y= and enter the expression
Press [2nd][MATH] to write the inequality
Press [2nd][MATH][
Step 2: Press [GRAPH].
The graph will be as given below:
Interpretation:
The graph of the equation
(e)
To calculate: The maximum and zeros of the function
Answer to Problem 74AYU
Solution:
Maximum of
Explanation of Solution
Given Information:
Calculation:
The equation of
To find the zeros and maximum of
Step 1: Press Y= and enter the expression
Step 2: Press [2nd][TRACE] to get the CALC. Under CALC menu choose 2: zero and press
ENTER.
Step 3: Move the cursor( use arrow keys ) to left of observed zero location. Press ENTER.
Step 4: Move the cursor( use arrow keys ) to right of observed zero location. Press ENTER.
Step 5: When the last screen asks for guess, press ENTER.
The coordinates of zeros are
As the distance and height should be positive, the co-ordinate of zero is
Step 6: Press [2nd][TRACE] to get the CALC. Under CALC menu choose 4: maximum and press
ENTER.
Step 7: Move the cursor( use arrow keys ) to left of observed maximum location. Press ENTER.
Step 8: Move the cursor( use arrow keys ) to right of observed maximum location. Press ENTER.
Step 9: When the last screen asks for guess, press ENTER
The coordinate of maximum value is
From part (b) the maximum height is
Hence, using graphical utility the maximum height and the zero of the function coincides with the answers from part (b) and part (c).
(f)
To calculate: The distance of projectile from the firing point, when it is 50 feet above the ground.
Answer to Problem 74AYU
Solution:
The distance of projectile from the firing point is
Explanation of Solution
Given Information:
A projectile is fired at an inclination of
Where
Formula used:
Calculation:
A projectile is fired at an inclination of
Where
The projectile is 50 feet above the ground.
The least common denominator is
Divide by
Add
The equation
The height of projectile is maximum at a distance
So, when the projectile is at height 50 feet above the ground the distance from firing point must be less than 156.25 feet.
The distance of projectile from the firing point is
Chapter 3 Solutions
Precalculus
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