4. A projectile is launched at an angle of 30° and lands 22 s later at the same heightas it was launched.a. What is the initial speed of the projectile?b. What is the maximum altitude?c. What is the range?d. Calculate the displacement from the point of launch to the position on itstrajectory at 16 s.

Answered: 4. A projectile is launched at an angle…

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 39E: The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle...

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4. A projectile is launched at an angle of 30° and lands 22 s later at the same height
as it was launched.
a. What is the initial speed of the projectile?
b. What is the maximum altitude?
c. What is the range?
d. Calculate the displacement from the point of launch to the position on its
trajectory at 16 s.

Expert Solution

Step 1

Given that

A projectile is launched at an angle of $30 °$ and lands 22 s later at the same height as it was launched.

(a) To find the initial speed of the projectile:

Using the time of flight formula,

$t = \frac{2 v_{0} \sin θ}{g} (22 s) = \frac{2 v_{0} \sin 30 °}{9.8 m / s^{2}} v_{0} = \frac{22 s \times 9.8 m / s^{2}}{2 \sin 30 °} v_{0} = \frac{215.6}{(2 \times \frac{1}{2})} m / s v_{0} = 215.6 m / s$

Thus, the initial velocity is 215.6 m/s.

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