Question

Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation h = ?16t + 160t + 120 models the h height at t seconds of the flare. How long will it take for the flare to hit the ground? (to the nearest tenth of a second)

Answer 1

Answer:

The time taken for the flare to hit the ground is approximately 10.7 seconds.

Step-by-step explanation:

Given : Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation $h =- 16t^2+ 160t + 120$ models the h height at t seconds of the flare.

To find : How long will it take for the flare to hit the ground?

Solution :

The equation  $h =- 16t^2+ 160t + 120$ models the h height at t seconds of the flare.

The flare to hit the ground when h=0.

Substitute in the equation,

$-16t^2+ 160t + 120=0$

Applying quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where, a=-16, b=160 and c=120

$x=\frac{-160\pm\sqrt{160^2-4(-16)(120)}}{2(-16)}$

$x=\frac{-160\pm\sqrt{33280}}{-32}$

$x=\frac{-160\pm 182.42}{-32}$

$x=\frac{-160+182.42}{-32},\frac{-160-182.42}{-32}$

$x=−0.70,10.70$

Reject the negative value.

Therefore, the time taken for the flare to hit the ground is approximately 10.7 seconds.