If a rock is propelled upward from the surface of Mars at a velocity of 93 m/sec, it reaches a height
s = 93t – 1.86t^2 after t sec.
a. Find the rock’s velocity and acceleration at time t.
v'(t)=93-3.72t
a''(t)=-3.73
b. How long does it take the rock to reach its highest point?
v'(t)= 93-3.72t=0
t=25s
c. How high does the rock go?
f(x)= 93(25)-1.86(25)^2=1162.5m
I couldn't find the last two.
d. How long does it take the rock to reach 1/4 of its maximum height?
e. How long is the rock aloft?
1 answer
a, b, and c look correct. For d, divide your answer from c by 4, plug it into the height equation, and solve for t. For e, it took 25 to reach the peak so it will take twice that long to reach 0 again (set s=0 and solve for t).
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