A golf ball is hit into the air. The path of the golf ball is represented by the function h equals 40 t minus 5 t squared, where h is the height of the ball in feet and t is the time in seconds.
How many seconds will it take the golf ball to reach a height of 60 feet?
Answer options with 4 options
A.
2
B.
3
C.
4
D.
8
To solve this question, we can set the height function equal to 60 and solve for t:
40t - 5t^2 = 60
5t^2 - 40t + 60 = 0
Now, we need to factor this quadratic equation. The factors of 5t^2 that multiply to 60 and add up to -40 are -10 and -6:
5t^2 - 10t - 6t + 60 = 0
5t(t - 2) - 6(t - 1) = 0
(5t - 6)(t - 10) = 0
Now, set each factor equal to 0 and solve for t:
5t - 6 = 0
5t = 6
t = 6/5
t = 1.2 seconds
t - 10 = 0
t = 10 seconds
So, the golf ball will reach the height of 60 feet at 1.2 seconds and 10 seconds. Since time cannot be negative, the answer is 1.2 seconds, which is not listed in the answer choices. Therefore, the closest option is 2 seconds (A) to the correct answer.