To find out how long it takes for Lukalu to reach the ground, we need to find the time at which her vertical position y(t) is equal to 0 (when she touches the ground).
Given the vertical position equation:
y(t) = -16t^2 + 100
Setting y(t) to 0 and solving for t:
0 = -16t^2 + 100
16t^2 = 100
t^2 = 100/16
t^2 = 6.25
t = √6.25
t = 2.5 seconds
So, it takes Lukalu 2.5 seconds to reach the ground.
To find out how far away from the cliff she is when she lands, we can use her horizontal position equation:
Given the horizontal position equation:
x(t) = 8t
Substitute t = 2.5 seconds into x(t) to find her distance from the cliff:
x(2.5) = 8(2.5)
x(2.5) = 20
Therefore, when Lukalu lands, she is 20 units away from the cliff.
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)=−16t^2+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.
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