Explanation:
An explosion causes debris to rise vertically with an initial velocity of 144 feet per second. The height as a function of time t is given by :
[tex]s(t)=-16t^2+144t[/tex]
t is in time in seconds
The speed of the debris is :
[tex]\dfrac{ds}{dt}=\dfrac{d(-16t^2+144t)}{dt}\\\\\dfrac{ds}{dt}=v=-32t+144[/tex] .......(1)
When it hits the ground, the distance covered is equal to 0 i.e. s(t)=0
So,
[tex]-16t^2+144t=0\\\\t(-16t+144)=0\\\\16t=144\\\\t=\dfrac{144}{16}\\\\t=9\ s[/tex]
It means at 9 seconds it will hit the ground.
Put t = 9 s in equation (1). So,
[tex]v=-32(9)+144\\\\v=-144\ m/s[/tex]
So, the the instantaneous speed of the debris when it hits the ground is (-144 m/s).
