# calculus

posted by .

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 -

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

## Similar Questions

1. ### physics

Wiley Coyote has missed the Road Runner once again. This time he leaves horizontally off the edge of the cliff at 25 m/s. If he hits the 400 m from the base of the cliff, how high is the cliff?
2. ### physics

A car was seen driving off the edge of a cliff at an angle of 10.° above the horizontal. The cliff is 95. m high and the car impacted the ground at a distance of 156. m from the base of the cliff. The speed of the car as it left the …
3. ### physics

A stone falls from a cliff. It lands on the ground below the cliff after 4.2 seconds. The height of the cliff can be calculated to be what?
4. ### Physics

A diver in Acapulco jumps off a 150 ft cliff. His forward motion is 10 feet per second. The base of the cliff at the waters edge extends 38 feet beyound the top edge of the cliff. Will the diver land in the water?
5. ### Physics

A diver in Acapulco jumps off a 150 ft cliff. His forward motion is 10 feet per second. The base of the cliff at the waters edge extends 38 feet beyound the top edge of the cliff. Will the diver land in the water?
6. ### Physics

A runner runs and jumps off a cliff into the water below. If the runner takes up running a 9.37 m/s and lands in the water 2.0 m away from the cliff's edge: How tall is the cliff?
7. ### physics

A rock falls off the edge of a cliff and strikes the ground after 3.8 s. What is the height of the cliff?
8. ### Physics

A baseball is hit off the edge of a cliff horizontally at a speed of 30 m/s. It takes the ball 3 seconds to reach the ground, with no air resistance. How high is the cliff wall?
9. ### Physics

A rock perched on the edge of a cliff falls off.  It starts from rest, and falls freely for 1.48 seconds before reaching the ground at the base of the cliff.   What is the speed of the stone just before it hits the ground?
10. ### Calculus

A hang glider is standing at the top of a 3,000 foot cliff. The hang glider jumps off and begins to descend at a constant rate of 50 feet per second, how fast is the area of the triangle formed by the cliff, the hang glider, and the …

More Similar Questions