Posted by **Martha** on Monday, November 12, 2012 at 10:25pm.

Wiley jumps straight up in the air from the edge of a cliff so that when he comes down he falls off the cliff. The cliff is 40 feet off the ground. His height t seconds after he jumps is s= -16t2 + 12t + 40.What is the maximum height? What is his maximum velocity?

- calculus -
**Reiny**, Monday, November 12, 2012 at 11:25pm
ds/dt = -32t + 12

= 0 for a max of s

32t = 12

t = 12/32 sec = 3/8 sec

for that time

s = -16(9/64) + 12(3/8) + 40

= 169/4 or 42.25 ft above the base of the cliff

when he hits the ground, s = 0

-16t^2 + 12t +40=0

divide by -4

4t^2 - 3t - 10 = 0

(t-2)(4t+5) = 0

t = 2 or t = -5/4, but t > 0

so he will hit the ground after 2 seconds

ds/dt = -32t+12

when t=2

ds/dt = -32(2) + 12 = -52 ft/sec

the negative indicates a downward direction, he is falling

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