Question

A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 96 ft per second. The function h(t)=96t-16t^2 gives the height of the falling debris above the ground, in feet, t seconds after the explosion. use the function to find the height of the debris one second after explosion (After 1 second the height is___)and how many seconds after the explosion with the debris hit the ground (___seconds)

Answer 1

a) 80feet

b) 6 seconds

Step-by-step explanation:

Given the formula that represents the height of the falling debris above the ground expressed as:

`h(t)=96t-16t^2`

In order to get the height of the debris one second after explosion, we will substitute t = 1sec into the formula as shown:

`\begin{gathered} h(1)=96(1)-16(1)^2 \\ h(1)=96-16 \\ h(1)=80ft \end{gathered}`

Hence the height of the debris one second after the explosion is 80feet

The debris hits the ground at the point where the height is 0 feet. Substitute h = 0 into the function as shown:

`\begin{gathered} 0=96t-16t^2 \\ -96t=-16t^2 \\ 16t^2=96t \\ 16t=96 \\ t=(96)/(16) \\ t=6secs \end{gathered}`

Therefore the debris hits the ground 6 seconds after the explosion