If we stand on top of a 170-foot building and throw a ball up into the air with an initial velocity of 25 feet per second, then the height of the ball above the ground is given by the following equation:
H = -16t^2 + 25t + 170
Here, t represents time in seconds, and H represents the height measured in feet.
(a) Complete the following table, giving the value of H at different time intervals:
t H
0 170
0.25 169.34
0.5 168.5
0.75 167.47
1 166.25
1.25 164.84
1.5 163.25
1.75 161.47
2 159.5
2.25 157.34
2.5 155
2.75 152.47
3 149.75
3.25 146.84
3.5 143.75
3.75 140.47
4 137
(b) Create a graph of H versus t from 0 to 4.
(c) Find the value of t that maximizes H. (Round your answer to two decimal places.)
t = 1.56 sec
(d) Find the maximum value of H. (Round your answer to two decimal places.)
H = 176.25 ft
Explain the meaning of the number in practical terms.
The maximum value of H represents the highest point the ball reaches above the ground during its trajectory.
(e) At what times t is the height of the ball 175 feet? (Round your answers to two decimal places.)
t = 1.47 sec (smaller value)
t = 2.53 sec (larger value)