SOLUTION: At 9:45 am Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation: h(t) = �0.6t2 + 108t + 75. a. Wh

Question 762872: At 9:45 am Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation: h(t) = �0.6t2 + 108t + 75.
a. What will be the maximum height of the ball? __________
b. How long will it take the ball reach its maximum height? __________
c. At what time will the ball hit the ground? _________

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation:
h(t) = �0.6t2 + 108t + 75.
---------------------
b. How long will it take the ball reach its maximum height?
The equation is of a parabola.
The max ht is the vertex.
The vertex is on the axis of symmetry, t = -b/2a
t = -108/(2*-0.6) = 90 seconds
==========
a. What will be the maximum height of the ball?
Max ht = h(90)
= -0.6*90^2 + 108*90 + 75
= 4935 ft
===========
c. At what time will the ball hit the ground?
When h(t) = 0
h(t) = �0.6t^2 + 108t + 75 = 0
6t^2 - 1080t - 750 = 0
t^2 - 180t - 125 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=32900 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 180.691785736085, -0.691785736085265. Here's your graph:

============
t =~ 180.69 seconds
Ignore the negative solution

RELATED QUESTIONS
at 9:45 am Maggie threw a ball upwards while standing on a platform 55 ft off of the... (answered by stanbon)

At 9:45am Margie threw a ball upwards while standing on a platform 65 ft above the... (answered by ewatrrr)

at 9:45am Margie threw a ball upwards while standing on a platform 35 ft. above the... (answered by Alan3354)

At 9:45 am Sue threw a ball upwards while standing on a platform 35 feet above the... (answered by stanbon)

Doug throws a ball vertically into the air while standing on a platform that is 10 feet... (answered by Boreal)

Bob threw a ball upward at a velocity of 10 m/s while standing on the roof of a building... (answered by htmentor)

Jacob is standing at the top of an 80 ft-high cliff and throws a rock upwards at 64... (answered by Edwin McCravy,ikleyn)

Rewrite the golf equation of h(x)=-16x^2+120x to show Marc hitting the ball while... (answered by Alan3354)

You threw a ball straight DOWN at an initial velocity of 32 ft/sec from a platform 384 ft (answered by ankor@dixie-net.com)