d) How long would it take the rock to reach half its maximum height? e) How long would the rock be aloft?

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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Only Solve part (d) and (e)

On Earth, in the absence of air, the rock
reach a height of s = 24t – 4.91² meters in t seconds.
a) Find the rock's velocity and acceleration at time t.
b) How long would it take the rock to reach its highest point?
c) How high would the rock go?
d) How long would it take the rock to reach half its maximum
height?
e) How long would the rock be aloft?
Transcribed Image Text:On Earth, in the absence of air, the rock reach a height of s = 24t – 4.91² meters in t seconds. a) Find the rock's velocity and acceleration at time t. b) How long would it take the rock to reach its highest point? c) How high would the rock go? d) How long would it take the rock to reach half its maximum height? e) How long would the rock be aloft?
Expert Solution
Step 1

Given that, the equation of the motion is s=24t-4.9t2.

The function attains the maximum of 29.388 at x=2.449.

d)

The half of the maximum height is 29.3882=14.694.

24t-4.9t2=14.694-4.9t2+24t-14.694=04.9t2-24t+14.694=0t=0.71729 or t=4.18066t=0.72 or t=4.18

Therefore, the time that the rock to reach the half of its maximum height is 0.72 seconds and 4.18 seconds.

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