Question
A rocket is launched from atop a 76-foot cliff with an initial velocity of 107 ft/s. The height of the rocket
above the ground at time t is given by .
A) When will the rocket hit the ground after it is launched? Round to the nearest tenth of a second.
(Solve Algebraically, Hint: Use the Quadratic Formula to solve and the round the square root answer one
decimal place)
B) When will the rocket reach 167ft from the ground?
above the ground at time t is given by .
A) When will the rocket hit the ground after it is launched? Round to the nearest tenth of a second.
(Solve Algebraically, Hint: Use the Quadratic Formula to solve and the round the square root answer one
decimal place)
B) When will the rocket reach 167ft from the ground?
Answers
The height equation that should have been given to you would be ...
height = -16t^2 + 107t + 76
"When will the rocket hit the ground". I will assume by ground you mean 76 below the cliff, so height = 0
-16t^2 + 107t + 76 = 0
16t^2 - 107t - 76 = 0
They told you to use the quadratic equation formula, so ...
t = (107 ± √(107^2 - 4(16)(-76)) )/32
= ..... you do the button pushing, use the positive result only
b)
-16t^2 + 107t + 76 = 167
16t^2 - 107t + 91 = 0
You will get 2 answers, both positive and both exact.
One will be the time it will reach a height of 167 on its way up, and the other
on its way down.
height = -16t^2 + 107t + 76
"When will the rocket hit the ground". I will assume by ground you mean 76 below the cliff, so height = 0
-16t^2 + 107t + 76 = 0
16t^2 - 107t - 76 = 0
They told you to use the quadratic equation formula, so ...
t = (107 ± √(107^2 - 4(16)(-76)) )/32
= ..... you do the button pushing, use the positive result only
b)
-16t^2 + 107t + 76 = 167
16t^2 - 107t + 91 = 0
You will get 2 answers, both positive and both exact.
One will be the time it will reach a height of 167 on its way up, and the other
on its way down.
A. V = Vo + g*Tr
0 = 107 + (-32)Tr
Tr = 3.34 s. = Rise time.
V^2 = Vo^2 + 2g*h.
0 = 107^2 + (-64)h
h = 178.9 Ft. above roof.
ho+h = 76+178.9 = 254.9 Ft. above gnd.
0.5g*Tf^2 = 254.9
16Tf^2 = 254.9
Tf = 4 s. = Fall time.
Tr + Tf = 3.34 + 4 = 7.3 s. = Time to reach gnd.
B. 0.5g*T^2 = 254.9-167
16T^2 = 87.9
2.3 s.
0 = 107 + (-32)Tr
Tr = 3.34 s. = Rise time.
V^2 = Vo^2 + 2g*h.
0 = 107^2 + (-64)h
h = 178.9 Ft. above roof.
ho+h = 76+178.9 = 254.9 Ft. above gnd.
0.5g*Tf^2 = 254.9
16Tf^2 = 254.9
Tf = 4 s. = Fall time.
Tr + Tf = 3.34 + 4 = 7.3 s. = Time to reach gnd.
B. 0.5g*T^2 = 254.9-167
16T^2 = 87.9
2.3 s.