More math...thanks for all your help, i'm stuck, just cant get it?

Question

a baseball is thrown from the top of a building and falls to the ground below. Its path is approximated by the relation h= -5t² + 5t +30, where h is the height above the ground in metres and t is the elapsed time in seconds.

1.draw a diagram that models this situation
2.how tall is the building
3.when will the ball hit the ground
4.when does the ball reach its maximum height
5.how high above the building is the ball at its maximum height

Answer 1

1. Can't draw on here - you're on your own.
2. The height of the building is found by calculating h when t = 0:

h = -5(0)^2 + 5(0) + 30 = 0 + 0 + 30 = 30

The building is 30 meters high.

3. The ball hits the ground when h = 0:
0 = -5t^2 + 5t + 30
0 = (-5t - 10)(t - 3)
t = -2, 3 (3 only logical solution)

The ball hit the ground at 3 seconds.

4. The ball reaches its maximum height when it reaches the top of its curve. At this instant the slope of the curve is zero. We can determine that point by determining when the derivative of the curve equals zero:

h'=-10t + 5
0 = -10t + 5
10t = 5
t = 0.5

The ball reaches its maximum height at 0.5 seconds.

5. The maximum height of the ball occurs at t = 0.5 (see #4), so we can calculate for h when t = 0.5:

h = -5(0.5)^2 + 5(0.5) + 30
h = -5(0.25) + 2.5 + 30
h = -1.25 + 32.5
h = 31.25

The maximum height of the ball is 31.25 meters. And since the building is 30 meters high, the ball is 1.25 meters above the building at its maximum height.

Now use all of this information to draw your diagram.

Answer 2

#1: This is a parabola moving upwards from the top of the building, curving downwards and hitting the ground.
#2: 30 meters. Note that the baseball is at the top of the building when t=0, and when t=0 its height is 30 meters.
#3: t=3 seconds. Find out when its height equals zero. Thus, -5t²+5t+30=0 → t²-t-6=0 → (t-3)(t+2)=0 → t=-2 or 3, but we want it it hit the ground _after_ we throw it, so t=3.
#4: t=0.5 seconds. To find the maximum of a function, set its derivative equal to zero. Thus, -10t+5=0 → t=1/2.
#5: 1.25 meters. Find the height of the ball, and subtract the height of the building. Thus the height is -5(0.5²) + 5(0.5) + 30 - 30 → -1.25 + 2.5 → 1.25 meters.