Question

Check on my answer please
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 = -16t^2 + 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.

A) 0 = -16t^2+101t+116; 8s
B) 0 = -16t^2+116t+101; 0.8s
C) 0 = -16t^2+101t+116; 0.8s
D) 0 = -16t^2+116t+101; 8s - my answer

Answer 1

after a substitution, we get:
\[\Large h = - 16{t^2} + 116t + 101\]

Answer 2

your answer is correct.

Answer 3

the rocket will reach its maximum height at time:
\[\Large {t_1} = \frac{{{v_0}}}{g} = \frac{{116}}{{32}} = 3.625\sec \]

Answer 4

and it will return on the earth surface at time:
\[\large {t_2} = \sqrt {{{\left( {\frac{{{v_0}}}{g}} \right)}^2} + \frac{{2{h_0}}}{g}} = 4.411\sec \]

Answer 5

so total time is:
\[\Large 3.625 + 4.411 \cong 8.04\sec \]

Answer 6

so, you are right!

Answer 7

I have applied the equation of dynamic!

Answer 8

thank you both :)

Answer 9

:)

Answer 10

@Michele_Laino you are good in Physics. ^__^

Answer 11

thanks! :) @ASAAD123