The units of measurements have not been supplied, so they will not be used. On the other hand, a 'common sense' check will not be possible without the units.
f(t) = 250t - 25t²
1. maximum height occurs when f'(t) = 0
f'(t) = 250 - 25*2t = 250 - 50t = 0
t= 250/50 = 5
f(5)
= 250*5 - 25*5²
= 1250 - 625
=625
2. Velocity
Velocity is f'(t).
When it hits the ground, solve for t when f(t)=0.
f(t) = 250t - 25t² = 0
t(250-25t) = 0
t=0 or t=10
f'(t) = 250 - 25*2t
f'(10) = 250 - 25*2*10 = 250 - 500 = -250
(equals the initial upwards velocity of 250 in magnitude).
A ball thrown up has a height f(t)=250t-25t^2 after t seconds.
(1) find the maximum height
(2) find the velocity when it hits the ground.
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