Answer:
A) 0 = -16t^2+135t+76
B) The rocket will take 9 seconds to hit the ground after it is launched.
Explanation:
We have given:
A rocket is launched from atop a 76-foot cliff with an initial velocity of 135 ft/s.
A) Substitute the values into the vertical motion formula h-16t^2+ vt+c.
Let h = 0
h= -16t^2+ vt+c
Lets substitute the values v= 135 and c = 76
h = -16t^2+135t+76
Now lets say h=0:
0 = -16t^2+135t+76
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.
The equation is:
0 = -16t^2+vt+c
0 = -16t^2+35t+76
Apply quadratic formula:
x = -b+/-√b^2-4ac/2a
t=-(135)+/-√(135)^2-4(-16)(76)/2(-16)
t = -135+/-√18225+4864/ -32
t=-135+/-√23089/ -32
t = -135+/-151.951 / -32
t = -135+151.951/ -32 , t = -135-151.951/ -32
t = 16.951/ -32 , t= -286.951 / -32
t= -0.5297 , t = 8.967
Therefore we will consider the value t=8.967 which is equivalent to 9 seconds when we rounded off. The other value is negative.
The rocket will take 9 seconds to hit the ground after it is launched....