A rock thrown verticll upward from the surface of the moon at a velocity of 40 m

Question

A rock thrown verticll upward from the surface of the moon at a velocity of 40 misec reaches a height of s -401-0.8f meters in tsec a. Find the rock's velocity and acceleration at time t b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft? a. Find the rock's velocity at time t v=| | m/s Find the rock's acceleration at time t. a | | m/s Simplify your answer. Use integers or decimals for any numbers in the expression) b. How long does it take the rock to reach its highest point? sec implify your answer.) C. How high does the rock go? (Si answer in f the answer boxes here to seare

Explanation / Answer

given s(t) = 40t - 0.8t2

a) velocity v = s'(t) = d/dt [ 40t - 0.8t2 ] = 40 - 1.6t

acceleration a = v'(t) = d/dt [ 40-1.6t ] = - 1.6

b) hightest point at v=0

40-1.6t = 0

t = 40/1.6 = 25 sec

c) s(25) = 500 m

d) 250 m ( half of maximum height

e) t = 2*25 = 50 sec

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