Question

A bullet is fired straight up from a gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula h = − 16 t 2 + v 0 t + 8 to determine how many seconds it will take for the bullet to hit the ground. (That is, when will h = 0 ?) Round your answer to 2 decimal places

Answer 1

Answer:

70 seconds

Step-by-step explanation:

Given that;

The initial velocity $v_o$ of the bullet fired = 1120 ft/s

Initial height h = 8 feet

The expression to determine how many seconds it takes the bullet to hit the ground is:

$h = -16t^2 +v_ot + 8$

Thus;

Replacing the value of $v_o$ =  1120 and h = 0 (i.e. when h =0) in the above expression; we have:

$0= -16t^2 +(1120)t + 8$

$= -16t^2 +(1120)t + (8-0)$

= -16t² + 1120t + 8

mulitiply through by (-)

= 16t² -1120t - 8

Divide through by 8

= 2t² -  140t - 1

The above expression forms a quadratic equation.

where;

a = 2

b = -140

c = - 1

So, by using the quadratic formula $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$, we have:

$= \dfrac{-(-140) \pm \sqrt{(-140)^2-4(2)(-1)}}{2(2)}$

$= \dfrac{140 \pm \sqrt{19600-(-8)}}{4}$

$= \dfrac{140 \pm \sqrt{19608}}{4}$

$= \dfrac{140 \pm 140}{4}$

$=\dfrac{140+ 140}{4} \ \ \ OR \ \ \ \dfrac{140-140}{4}$

$=\dfrac{280}{4} \ \ \ OR \ \ \ 0$

= 70

Thus, the time (in seconds) it took the bullet to it the ground = 70 seconds