COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 3, Problem 62QAP
To determine
How long Aaron must wait to throw the ball, so that Jordy can catch it at the same height as it was thrown.
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Problem
For a projectile lunched with an initial velocity of v0 at an angle of θ (between 0 and 90o) , a) derive the general expression for maximum height hmax and the horizontal range R. b) For what value of θ gives the highest maximum height?
Solution
The components of v0 are expressed as follows:
vinitial-x = v0cos(θ)
vinitial-y = v0sin(θ)
a)
Let us first find the time it takes for the projectile to reach the maximum height.
Using:
vfinal-y = vinitial-y + ayt
since the y-axis velocity of the projectile at the maximum height is
vfinal-y = ?
Then,
? = vinitial-y + ayt
Substituting the expression of vinitial-y and ay = -g, results to the following:
? = ? - ?t
Thus, the time to reach the maximum height is
tmax-height = ?/?
We will use this time to the equation
yfinal - yinitial = vinitial-yt + (1/2)ayt2
if we use the time taken to reach the maximum height, therefore, the displacement will yield the maximum height, so
hmax = vinitial-yt + (1/2)ayt2
substituting, the vinitial-y…
Chapter 3 Solutions
COLLEGE PHYSICS
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