Question

Charlize wants to measure the depth of an empty well. She drops a ball into the well and measures how long it takes the ball to hit the bottom of the well. She uses a stopwatch, starting when she lets go of the ball and ending when she hears the ball hit the bottom of the well. The polynomial h=-16t^2+6 represents how far the ball has fallen after t secondsA) how far has the ball fallen after one second? B) Charlize’s stopwatch measured a time of 3.2 seconds when the ball hit the bottom of the well. How deep is the well?

Answer 1

SOLUTION

A. how far the ball has fallen after 1 second

We will use the function to do this, using t = 1. This becomes

$\begin{gathered} h=-16t^2+6 \\ h=-16(1)^2+6 \\ h=-16+6 \\ h=-10 \end{gathered}$

So in 1 second, the ball has fallen 10 units

B. We will also find the depth of the well using the function. But here,

t = 3.2 seconds

$\begin{gathered} h=-16t^2+6 \\ h=-16(3.2)^2+6 \\ h=-16\times10.24+6 \\ h=-163.84+6_{} \\ h=-157.84 \end{gathered}$

So the depth = 157.84 units