Function Question

[Hockeyman]

Hello again everbody. Here is the question

The roadrunner is standing at the edge of a cliff 800 meters above the ground. Wile E. Coyote is 42 meters above the ground on a ledge directly below the roadrunner. Wile E. has purchased a spring catapult from the acme catapult company. This catapult will propel Wile E upward with an initial velocity of 117 meters per second. The equation that gives the height h, of Wile E. above the ground t seconds after he releases the catapult is given

h(t)= -4.9t^2 + 117t + 42

Now the question

Wile E gets a stronger catapult. catapults come in integer strenghts each increase of one meter per second initial velocity costs $100. How much will Wile E. have to pay for a catapult strong enough to reach the roadrunner.

Now i did guess and check. In the equation i kept plugging in higher velocities and found the new maximum of the parabola. I found that 118.5 was the closest to 800 meters, its maximum height was about 800.44 meters with the initial height of 42 meters. Is this correct. Therefore he would have paid 150 dollars.

 

[skeeter]

when you started 'fiddling' with the initial velocity, did you take into account that time also changes?

at the top of his trajectory, the coyote's velocity will be 0.
he will experience a downward acceleration of 9.8 m/s² on the way up.
he needs to rise 758 m.

using the mo' better equation ...
\(\displaystyle v_f^2 = v_o^2 - 2g(\Delta y)\)
... note that 'time' is absent from this equation.

\(\displaystyle v_f = 0\)
\(\displaystyle g = 9.8 m/s^2\)
\(\displaystyle \Delta y = 758 m\)

\(\displaystyle 0 = v_o^2 - 2(9.8)(758)\)

\(\displaystyle v_o = \sqrt{2(9.8)(758)} \approx 122 m/s\)

looks like about $500

 

[Hockeyman]

I'm not entirely sure what you mean, i understand that the amount of time it takes him to get to his maximum height increases, but i'm not sure what you are saying. I'm sorry.