Question

A pilot of a helicopter plans to release a bucket of water on a forest fire. The height y in feet of water t seconds after its release is modeled by y = − 16 t 2 − 2 t + 400 . How long will it take for the water to reach the ground? Round to one number after the decimal point.

Answer 1

4.93 seconds

Explanation:

The height y in feet of water t seconds after its release is given by the equation as follows :

`y=-16t^2-2t+400`

We need to find the taken taken for the water to reach the ground. When it reach the ground, y will be equal to 0. So,

`-16t^2-2t+400=0`

Above is a quadratic equation whose solutions can be calculated as follows :

`t=(-(-2)\pm √((-2)^2-4* (-16)* 400) )/(2* (-16))\\\\t=(-(-2)+ √((-2)^2-4* (-16)* 400) )/(2* (-16)), (-(-2)- √((-2)^2-4* (-16)* 400) )/(2* (-16))\\\\t=-5.062\ s\ \text{and}\ 4.93\ s`

Neglecting negative value.

Hence, it will take 4.93 seconds for the water to reach the ground