Bob the Iguana is waiting to use his Giant slingshot to shoot Evil Bart the Blac
ID: 3187893 • Letter: B
Question
Bob the Iguana is waiting to use his Giant slingshot to shoot Evil Bart the Blackbird out of the sky as he flies overhead. Bob's giant slingshot launches a stone vertically so that the function h(t)=300t-16t^2 models the height h in feet of the stone t seconds after it leaves the slingshot. (Do not use physics to answer the question)a.) Bart the Blackbird is flying at a constant height of (1/4) of a mile and a constant speed of 10 ft/sec. Assuming that Bob times his shot correctly, can he hit Bart?
--I set the original equation to 1320ft=300t-16t^2 and set it equal to zero then used the quadratic equation to see if the solutions were positive therefore he can indeed reach the bird.
b.) Now assume that Bart flies at a constant height of 1000 feet and a constant speed of 10 ft/sec. When should Bob release the slingshot so that he can knock Evil Bart the Blackbird out of the sky?
--I think I need to solve for t, but I am not sure or how.
c.) With what velocity will the stone hit Bart?
---I think you simply take the derivative of the original equation.
Explanation / Answer
A)
To find the maximum height, we take the derivative and set it to 0, solve for t, and then plug that value into the original equation.
Like this:
h(t)=300t-16t^2
h'(t) = 300 - 32t
0 = 300 - 32 t
t = 300/32 = 9.375 s
h(9.375) = 300(9.375)-16(9.375)^2 = 1406.25 ft
Since this is greater than 1320, he can hit the bird.
B)
The equation governing the height of the rock is:
h(t)=300t-16t^2
Solve for h(t) = 1000
1000 = 300t - 16t^t^2
(just use the quadratic equation to solve this)
That gives us:
t = (5/8)(15 - sqrt(65))4.336 s
or
t = (5/8)(15+sqrt(65))14.414 s
So he should release it either 4.336 s or 14.414 s before the bird is right over his head.
Since bart travels at 10 ft/s this is when:
Bart is 43.36 ft away (horizontally not vertically) or 144.14 ft away (again horizontally)
C)
Take h'(t) and plug in the time calculated before:
h'(t) = 300 - 32t
h'((5/8)(15 - sqrt(65))) = 300 - 32*(5/8)(15 - sqrt(65))161.25 ft.s