Q:

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. a rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.a. substitute the values into the vertical motion formula h = −16t2 + vt +c. let h = 0.b. use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. round to the nearest tenth of a second.

Accepted Solution

A:
given that a rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.
a] substitutng the values into the vertical motion formula h = −16t2 + vt +c
we shall have:
v=116 ft/s
c=101
thus
h(t)=-16t^2+116t+101

b] The time taken for the rocket to hit the ground will be evaluated as follows:
let h=0
thus
h(t)=-16t^2+116t+101
0=-16t^2+116t+101
solving the quadratic equation using quadratic formula we obtain:
t=29/8+/-sqrt(1245)/8
thus
t=8.04 sec or -0.79
but since there is no negative time, we shall take t=8.04 seconds
Thus the rocket hit the ground after 8.04 sec