if an object is dropped from a height of 144 ft, the function h(t)=-16t^2+144 gives the height of the object after t seconds when will the object hit the ground?
A ) 1.5 s
B ) 3 s
C ) 6 s
D ) 9 s
To find out when the object hits the ground, we need to determine when its height is equal to zero.
Substitute h(t) = 0 into the function and solve for t:
-16t^2 + 144 = 0
Divide both sides of the equation by -16:
t^2 - 9 = 0
Factor:
(t - 3)(t + 3) = 0
Set each factor equal to zero and solve for t:
t - 3 = 0 or t + 3 = 0
t = 3 or t = -3
Since time cannot be negative in this context, we discard t = -3. Therefore, the object will hit the ground at t = 3 seconds.
Therefore, the correct answer is B) 3 s.