Question

A rock falls off a balcony. It’s height(in feet)is given by the formula f(x)= -16t^2+12.5t+150, where t is measured in seconds. How long will it take the rock to hit the ground?

Answer 1

Answer: $3.47\ seconds$

Step-by-step explanation:

Given the following function:

$f(x)= -16t^2+12.5t+150$

You need to follow these steps in order to solve the exercise:

1. Substitute $f(x)=0$:

$0= -16t^2+12.5t+150$

2. Now you need to apply the Quadratic formula. This is:

$x=t=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

In this case, you can identify that:

$a=-16\\b=12.5\\c=150$

Then, you can substitute these values into the formula:

$t=\frac{-12.5\±\sqrt{(12.5)^2-4(-16)(150)}}{2(-16)}$

3. Evaluating, you get:

$t_1=3.47\\\\t_2=-2.69$

4. You must choose the positive value. Then:

$t=3.47\ seconds$