The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
After how many seconds does the object reach its maximum height?
A. 2 seconds
B. 3 seconds
C. 6 seconds
D. 9 seconds
Answers
Given : The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon.
The maximum height reached by the object is 150 feet.
To Find : After how many seconds does the object reach its maximum height?
A. 2 seconds
B. 3 seconds
C. 6 seconds
D. 9 seconds
Solution:
function h(t) = –16t² + 96t + 6
max height = 150
=> –16t² + 96t + 6 = 150
=> –16t² + 96t - 144 = 0
=> t² - 6t + 9 = 0
=> ( t - 3)² = 0
=> t = 3 sec
After 3 seconds does the object reach its maximum height
Even if maximum height is not given still time can be found
h(t) = –16t² + 96t + 6
=> h'(t) = -32t + 96
h'(t) = 0
=> t = 3
h''(t) = - 32 < 0
Hence maximum height at t = 3
and by putting t = 3 max height = 150 feet
Learn More:
The daily cost of operating a hospital is a linear function of the ...
brainly.in/question/18029822
The height, y, of an object thrown into the air is known to be given by ...
brainly.in/question/12040785