Question

lariano is standing at the top of a hill when he kicks a soccer ball up into the air. The height of the hill is h feet,nd the ball is kicked with an initial velocity of v feet per second. The height of the ball above the bottom of theill after t seconds is given by the polynomial -16P? + vt + h. Find the height of the ball after 4 seconds if it wasicked from the top of a 25 foot tall hill at 72 feet per second.O 25 ftO 121 ftO 59 ftO 57 ft

Answer 1

We know that the height is given by the equation:

$h(t)=-16t^2+vt+h_0$

in this case the initial velocity is 72 ft/s and the inital height is 25 ft. Plugging this values the height function for the ball is:

$h(t)=-16t^2+72t+25$

If we want to know the height after 4 seconds we evaluate the function at t=4, then we have:

$\begin{gathered} h(4)=-16(4)^2+72(4)+25 \\ h(4)=57 \end{gathered}$

Therefore the height of the ball after four seconds is 57 ft.