Boris throws a ball vertically upward from the top of a cliff. The height of the hall above the base of the cliff is approximated by the model h=65+10t-5t^2, where h is the height in metres and t is the time in seconds.

Question

Boris throws a ball vertically upward from the top of a cliff. The height of the hall above the base of the cliff is approximated by the model h=65+10t-5t^2, where h is the height in metres and t is the time in seconds.
a. How high is the cliff?
b. How long does it take for the ball to reach a height of 5om above the base of the cliff?
C. After how many seconds does the ball hit the ground?

For (a) I got 65metres, For (b) I got 3secs BUT I DO NOT KNOW THE ANSWER TO C .
PLS HELP

Damon · Answer

a is obvious
b 5 = 65 + 10 t -5 t^2

5 t^2 - 10 t - 60 = 0
t^2 -2 t -12 = 0
t = [ 2 +/- sqrt (4+48)]/2
= 1 +/- sqrt 13
= 4.61 seconds

c
0 = 65 + 10 t - 5 t^2
t^2 -2 t -13 = 0
t = [ 2 +/- sqrt(4+52)]/2
= 1 +/- sqrt(14)
=4.74 sec