If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is [tex]-16t^{2} +48t[/tex].
We are required to find the time that the ball took to travel before returning the ground.
We know that speed is the distance a thing covers in a particular time period.
The height of the ball after t seconds is as follows:
h(t)=[tex]-16t^{2} +48t[/tex]
It is at ground at the instants of t.
Hence,
[tex]-16t^{2} +48t[/tex]=0
-16t(t-3)=0
We want value of t different of 0, hence :
t-3=0
t=3.
Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
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