Parabola word problem

Question

The height of a football is given in meters, y, and represented by the function y = -30x^2 + 5x where x is the time in seconds after the ball was kicked.

a) What is the height that the ball reached?

b) How long did it take the ball to hit the ground?

c) How long after it was kicked is that ball at 25 meters?

d) Why is there no constant?

Answer 1

y=-30x^2 + 5x

max height is when y'=0 =-60x +5, x=5/60 = 1/12th of a second

max y = -30(1/12)^2 +5/12 =-30/144 + 5/12

=5/12 -15/72

=5/12 -5/24

= 10/24 -5/24

= 5/24 feet high

= 2 1/2 inches

it hits the ground when y=0=-30x^2+5x

-5x(6x-1), x= 1/6 of a second

if it reaches 25 meters horizontally, that happens at any time less than or= 1/6 of a second

less than or = 150 meters per second is the horizontal velocity, which seems impossible.

so it never reaches 25 meters vertically or horizontally

it reached max height in half that time, x= 1/12 of a second

there is no constant because the constant = the initial height of the ball and apparently it is on the ground when kicked

this problem might be more realistic if the equation were y=-3.0x^2 +5x, moving the decimal point one digit left