A rock thrown vertically upward from the surface of the moon at a velocity of 8
ID: 2871895 • Letter: A
Question
A rock thrown vertically upward from the surface of the moon at a velocity of 8 m/sec reaches a height of s=8t-0.8t^2.
A rock thrown vertically upward from the surface of the moon at a velocity of 8m/sec reaches a height s=8t-0.8t^2 meters in t sec.
Find the rock's velocity and acceleration at time t.(The acceleration in this case is the acceleration of gravity on the moon.)
How long does it take the rock to reach its highest point?
How high does the rock go?
How long does it take the rock to reach half its maximum height?
How long is the rock aloft?
Explanation / Answer
A rock thrown vertically upward from the surface of the moon at a velocity of 8m/sec reaches a height s=8t-0.8t^2 meters in t sec.
Find the rock's velocity and acceleration at time t.(The acceleration in this case is the acceleration of gravity on the moon.) velocity=ds/dt=8-0.8*2*t=8-1.6t ,acceleration =dv/dt=-1.6
How long does it take the rock to reach its highest point?
maximum point==>ds/dt =0 ==>8-1.6t =0==>t=8/1.6==>t=5sec
How high does the rock go? s(5) =8*5 -0.8(5)^2
s(5) =40 -(0.8*25)
s(5) =40 -(20)
s(5) =20
How long does it take the rock to reach half its maximum height?
20/2 =8t-0.8t^2
8t-0.8t^2 =10
t-0.1t^2 =10/8
10t-t^2 =100/8
t^2 - 10t +12.5 =0
t=(10+(102-4*12.5))/2
t=(10+(100-50))/2
t=(10-50)/2,(10+50)/2
t=1.46sec ,8.54sec
t should be <5
==>t=1.46sec
How long is the rock aloft?
5+5 =10sec
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.