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
ds/dt = -32(2) + 12 = -52 ft/sec
the negative indicates a downward direction, he is falling
Answer This Question
More Related Questions
- physics - A rock falls off the edge of a cliff and strikes the ground after 3.8 ...
- Physics - A diver in Acapulco jumps off a 150 ft cliff. His forward motion is 10...
- Physics - A diver in Acapulco jumps off a 150 ft cliff. His forward motion is ...
- physics - Wiley Coyote has missed the Road Runner once again. This time he ...
- physics - A car was seen driving off the edge of a cliff at an angle of 10.° ...
- Physics - You are driving off of a horizontal cliff, and your car has a ...
- Physics - A car acchdently rolls off a cliff.as it leaves the cliff it has a ...
- Physics - A runner runs and jumps off a cliff into the water below. If the ...
- physics - a car accidently roll off a cliff. as it leaves the cliff it has a ...
- Physics - You are driving off of a horizontal cliff, again!!! The cliff is ...