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.pt2+100t+10.

 

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

 

2. What Wile E. coyote's maximum height? Does he reach the Roadrunner?

 

3. When is Wile E. Coyote at the same height as when he was catapulted?

 

4. When does Wile E. coyote land on the ground

 

5.Wile E. Coyote goes back to the ACME Company to get a stronger catapult. captapults come in integer strengths;each increases of one foot per second initial velocity costs $50. How much money will Wile E. Coyote have to spend to reach the Roadrunner?

 

6. since Wile E. coyote only has $200 to spend to buy the extra strength right now, he must think of another way to make his original catapult work. What can he do? Think about changing the original equation. Describe what the change would be. 

Answer 1

Question 1

 

Wile E needs to be at the same height as the road runner in order to catch him.  So we take the difference between their elevations to find his maximum height.

 

570ft - 10ft = 560 ft

 

His maximum height is h(t) = 560 ft

 

We set the equation to solve for t.

 

560 = -4t² + 100t + 10

 

I am not sure if your equation from the problem is written correctly, so I will let you complete this step after you make that correction.

 

 

Question 2 ties into question 1.

 

 

Question 3

 

Wile E was catapulted from his initial position 10ft.  We set the equation

 

10 = -4t² + 100t + 10

 

Solve for t.

 

 

Question 4

 

When he lands on the ground, his position will be h(t)=0.  We set the equation

 

0 = -4t² + 100t + 10

 

Solve for t.

 

 

Question 5

 

Since v₀ = 1 m/s  cost $50, and our v₀ = 100 m/s, multiply 50 by 100. 

 

Wile E would need to spend $5000.

 

 

Question 6

 

He would need to increase his initial position since the affect of gravity will likely decrease his speed, even if he were to get a stronger catapult.