Solve the solution.

Question

Solve the solution.

 

If a football is kicked straight up with an initial velocity of 128 ft/sec from a height of 4ft, then it's height above the earth is a function of time given by H(t) = -16t^2 - 128t - 4.

 

 

what is the maximum height reached by the ball.  ?  ft

Answer 1

Hi Keith;

H(t) = -16t^2 - 128t - 4.

This is a parabola.  Because the coefficient of the exponent is negative, it faces down.  The vertex is maximum.

x-value of vertex is -b/2a...

x=--128/[(2)(-16)]

x=128/-32

x=-4

Let's establish the y-value of the coordinate...

H(-4) = -16t^2 - 128t - 4.

H(-4) = -16(-4²) - [128(-4)] - 4.

H(-4)=[(-16)(16)]+512-4

H(-4)=-256+512-4

H(-4)=252

Vertex is (-4,252)

When t is -4, the height is 252 feet.

Obviously, something is wrong with the equation.