Answer:
The ball hits the ground after 7.6 sec.
Explanation:
Realize that h = 0 when the rocket hits the ground. Thus, we set h(t) = y = to 0 and solve for time (t):
y = 0 = h(t) = -16t^2 + 113t + 65.
Application of the quadratic formula is the easiest approach here. Note that a = -16, b = 113 and c = 65.
The discriminant is b^2-4ac, or, in this case, 113^2 - 4(-16)(65) = 16929.
Because the discriminant is positive, we confirm that this equation has two real, unequal roots.
The time values are as follows:
-113 ± √16929
t = --------------------- = -17.11/ (-32) sec, which we must reject
-32
because time in
this situation may not be (-).
The other root is:
-113 ± √16929
t = --------------------- = 7.6 sec
-32
The ball hits the ground after 7.6 sec.