Question

a football is kicked into the air with an initial upward velocity of 82 feet per second its height H in feet is recorded at various second in the table below write an equation for the curve of best fit than estimate the height of the football after 5 Seconds​

Answer 1

We have been given that a football is kicked into the air with an initial upward velocity of 82 feet per second. The height (H) of ball in feet is recorded at various second in the table. We are asked to write an equation that represents the given scenario.

We know that equation of height of an upward moving object is $h(t)=-\frac{1}{2}gt^2+V_0t+h_0$, where,

g = Acceleration due to gravity,

$V_0$ = Initial velocity,

$h_0$ = Initial height.

$V_0=82$ and $h_0=0$. We know that acceleration due to gravity is a constant and its value is 32 feet square per sec.

Upon substituting these values, we will get:

$h(t)=-\frac{1}{2}(32)t^2+82t+0$

$h(t)=-16t^2+82t$

Therefore, the equation $h(t)=-16t^2+82$ represents the height of the football after t seconds.

To find the height of the football after 5 seconds, we will substitute $t=5$ in our equation as:

$h(5)=-16(5)^2+82(5)$

$h(5)=-16(25)+410$

$h(5)=-400+410$

$h(5)=10$

Therefore, the height of the football after 5 seconds would be 10 feet.