Firing a Missile The initial speed of a missile is 330 m/s.
- (a) At what angle should the missile be fired so that it hits a target 10 km away? (You should find that there are two possible angles.) Graph the missile paths for both angles.
- (b) For which angle is the target hit sooner?
(a)
The angle of the missile to be fired that hits a target 10 km away and the graph of the missile paths for both angles.
Answer to Problem 4P
The angle of the missile to be fired that hits a target 10 km away is
Explanation of Solution
Given:
The initial speed of a missile is 330 m/s and the distance of the missile from the target is 10 km.
Formula used:
The formula of the parametric equations for the path of the particle with gravity and an angle
And
Calculation:
Consider the initial speed be
The given distance of the missile from the target is 10 km.
Convert km into m.
Substitute 330 m/s for
Substitute 330 m/s for
Multiply both sides by
Calculate
Thus, the angle of the missile to be fired that hits a target 10 km away is
Sketch the graph of both paths of the missile.
Figure (1)
Thus, Figure (1) shows the graph of both the paths of the missile.
(b)
The angle at which the target hits sooner.
Answer to Problem 4P
The smaller angle at which the target hits sooner is
Explanation of Solution
Given:
The initial speed of a missile is 330 m/s and the distance of the missile from the target is 10 km.
Calculation:
The angles of the missile to be fired that hits a target 10 km away is
The smaller angle is the angle at which target hits sooner.
Thus, the smaller angle at which the target hits sooner is
Chapter 8 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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