Concept explainers
(a)
To find: the time the bullet hits the ground
(a)
Answer to Problem 42E
The bullet hits the ground after
Explanation of Solution
Given:
Initial speed of
Angle =
Calculation:
A bullet is fired with angle of elevation
Find the time
The position of the bullet after
Here,
The path of the bullet is shown below.
Substitute
Then, the position of the bullet after
Impact occurs when the y-component of the parametric equations is zero.
Either
Here
So, take
Therefore, the bullet hits the ground after
Conclusion:
Therefore, the bullet hits the ground after
(b)
To find: the distance taken by the bullet to hit the ground
(b)
Answer to Problem 42E
The bullet hit the ground about
Explanation of Solution
Calculation:
Find the horizontal distance
The horizontal distance
From part
So, find the value of
Therefore, the bullet hit the ground about
Conclusion:
Therefore, the bullet hit the ground about
(c)
To find: the maximum height attained by the bullet
(c)
Answer to Problem 42E
The maximum height attained by the bullet is
Explanation of Solution
Calculation:
Find the maximum height attained by the bullet.
The position of the bullet after
First show that the path of the projectile is a parabola by eliminating the parameter
From the equation
Substitute
So, the equation
Compare the equation
Here,
The highest point on a parabola has
So,
Find the
Therefore, the maximum height attained by the bullet is
Conclusion:
Therefore, the maximum height attained by the bullet is
Chapter 8 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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