Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Lukalu is rappelling off a cliff. The parametric equations that describe her horizontal and vertical position as a function of time are x(t)=8t and y(t)=−16t2+100 and . How long does it take her to reach the ground? How far away from the cliff is she when she lands? Remember to show all of the steps that you use to solve the problem. (3 points)

Answer 1

To find out how long it takes for Lukalu to reach the ground, we need to figure out when y(t) = 0 since y(t) represents her vertical position.

-16t^2 + 100 = 0
-16t^2 = -100
t^2 = 100/16
t^2 = 6.25
t = √6.25
t = ±2.5

Since time cannot be negative, Lukalu takes 2.5 seconds to reach the ground.

To find out how far away from the cliff she is when she lands, we need to find her horizontal position at t = 2.5.

x(2.5) = 8(2.5)
x(2.5) = 20

Therefore, Lukalu is 20 units away from the cliff when she reaches the ground.