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.
Answers
Kasey
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
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
Apryl
Thank you so much!!
Correction Man
Actually the it is NOT 20 feet traveled kasey, you forgot to cancel out 2.5 on other side of the equation by dividing 20 by 2.5 and then you will get the CORRECT answer of x=8 feet traveled horizontally before hitting the ground safely which was t=2.5 seconds. Those are your actual answers guys.
Are you sure?
Actually Correction Man, the t on the other side of the equation has nothing to do with solving it, because the equation can just as easily be just y=16t^2+100 or x=8t. So Kasey is correct. The answer is x=8(2.5) which is x=20