Question

A bullet is fired straight up from a gun with the initial velocity 1120 feet per second at an initial height of 8 ft. Use the formula to determine how many seconds for the bullet to hit the ground. It will take __ seconds

Answer 1

In order to find the moment t, in seconds, when the bullet hits the ground, we need to use

h = 0

v₀ = 1120

in the given formula:

`\begin{gathered} h=-16t^2+v_0t+8 \\ \\ 0=-16t^2+1120t+8 \end{gathered}`

Now, we can solve the above equation using the quadratic formula:

`\begin{gathered} t=\frac{-1120\pm\sqrt[]{1120^2-4(-16)(8)}}{2(-16)} \\ \\ t=\frac{-1120\pm\sqrt[]{1254400+512}}{-32} \\ \\ t=\frac{-1120\pm\sqrt[]{1254912}}{-32} \\ \\ t=35\pm\sqrt[]{(2451)/(2)} \\ \\ t_1\cong70.01 \\ \\ t_2\cong-0.01 \end{gathered}`

Since the time must be positive, the answer is t₁. Therefore:

It will hit the ground after 70.01 seconds.