analyzing quadratic models

Question

question: the roadrunner is standing under the edge of a cliff 570 feet above the ground. Wile E. Coyote is 10 feet above the ground on a ledge directly below the Roadrunner. Wile E. has purchased a spring catapult from ACME catapult company. this catapult will propel Wile E. coyote upward with an initial velocity 100 feet per second. the equation that gives the height, h,of Wile E. coyote above the ground t seconds after he releases the catapul is given: h(t)= -4.9tsquared +100t+10.

 

question 1.  When does Wile E. coyote reach the maximum height?

Answer 1

Hi Stephan:

 

Needs clarification - Isn't RoadRunner standing "on" the edge of the cliff (as opposed to under)?

Also, be careful... looks like you have a mixed up quadratic equation for motion using meters/s and feet (seeing the 4.9 which is 1/2 of 9.8m/secsquared - acceleration due to gravity.    [Note:  h(t)- 1/2at² + V_ot + h₀]

 

First, we'll need to do some conversion... 1m = how many feet?  use that value to change your h(t) equation to something like:

 

h(t) = -16*tsquared+100t +10     

 

so at  t = 3.1s the height is maximized (calculus gives hmax is where -32t = -100) and at this time WEC will have reached a height of about 164m.  Gotta love that Coyote, but he needs a springier spring! 

 

Please let me know if that helps, especially in regards to:

1) word problem clarity and

2) unit consistency