Posted by **Kiley** on Sunday, February 10, 2013 at 9:16pm.

A ball is tossed straight upward with an initial velocity of 80 ft per second from a rooftop that is 12 feet above ground level . The height of the ball in feet at time t seconds is given by h(t)= -16t^2 +80t+12 find maximum height above ground level the ball reaches

- Math -
**Reiny**, Sunday, February 10, 2013 at 9:51pm
If you know Calculus,

h ' (t) = -32t + 80

= 0 for a max height

t = 80/32 = 5/2 or 2.5 seconds

h(2.5)= -16(2.5)^2 + 80(2.5) + 12

= 112 ft

If you don't know calculus, let's complete the square

h(t) = -16(t^2 - 5t **+ 25/4 -25/4 ** + 12

= -16( (t-5/2)^2 - 25/4) + 12

= -16(t-5/2)^2 + 100 + 12

= -16(t-5/2)^2 + 112

the vertex is (5/2 , 112)

so the max of h is 112 , when x = 5/2 as above

## Answer this Question

## Related Questions

- Math - Please help if you can. If a ball is shot projected straight upward at a ...
- math - An object that is falling or vertically projected into the air has it ...
- Math- - A ball is thrown vertically upward with an initial velocity of 96 feet ...
- pre-calc - Physics: a ball is thrown vertically upward with an initial velocity ...
- math - A robotic basketball player tosses a ball upward from a height of 7 feet...
- Algebra - THe function h(t)=-16t^2+v0t+h0 describes the height in feet above the...
- Algebra - THe function h(t)=-16t^2+v0t+h0 describes the height in feet above the...
- Algebra - word problem - A red ball and a green ball are simultaneously tossed ...
- Math - You throw a ball into the air with an initial vertical velocity of 31 ...
- Pre-Calculus - A ball is thrown vertically upward with an initial velocity of 64...