Precalculus Question #1

Question

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.

Answer 1

For Y, since the "ground" Is assumed to be when y(t) = 0, you want to solve for t.

0=-16t^2+100

16t^2=100

t^2=100/16

t^2=6.25

t=2.5seconds

Now that you know t, which is how long it takes to get to the ground, you can plug it into x(t) to find out the horizontal distance traveled

x(t)=8t

x(2.5)=8*2.5=20 feet