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 ) = 8 t and y ( t ) = − 16 t 2 + 100 and . How long does it take her to reach the ground? How far away from the cliff is she when she lands?

Answer 1

2.5 s, 5 m

Step-by-step explanation:

The equations for the horizontal and vertical position of Lukalu are:

`x(t) = 8t\\y(t) = -16t^2 + 100`

we can find the time it takes her to reach the ground by requiring that the vertical position becomes zero:

y(t) = 0

So we find:

`0=-16t^2 +100\\16t^2 = 100\\t=\sqrt{(100)/(16)}=2.5 s`

The horizontal distance of Lukalu instead will be given by the equation for the horizontal position, substituting t = 2.5 s:

`x=8t = 8 \cdot 2.5 s =5 m`