MATH SOLVE

3 months ago

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= -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.

Accepted Solution

A:

Here the vertical motion formula is h = -16t^2 + 116t + 101 (feet)

How long will it take for the rocket to rise, stop rising, start falling and then his the ground? To find this, set h = 0 and solve for t. Omit negative results, if any.

-16t^2 + 116t + 101 = 0.

Since the solutions are unlikely to be "nice" numbers (integers), let's use the quadratic formula to solve this equation for t:

-116 plus or minus sqrt(116^2 - 4(-16)(101) )

t = ----------------------------------------------------------------

2(-16)

-116 plus or minus sqrt(19920)

= ---------------------------------------------

-32

-116 plus or minus 141.1

= -----------------------------------

-32

= -25.1/(-32) (discard) and t = -116 - 141.1

------------------

-32

t = 8.03.

The rocket will hit the ground 8.03 seconds after it is launched.

How long will it take for the rocket to rise, stop rising, start falling and then his the ground? To find this, set h = 0 and solve for t. Omit negative results, if any.

-16t^2 + 116t + 101 = 0.

Since the solutions are unlikely to be "nice" numbers (integers), let's use the quadratic formula to solve this equation for t:

-116 plus or minus sqrt(116^2 - 4(-16)(101) )

t = ----------------------------------------------------------------

2(-16)

-116 plus or minus sqrt(19920)

= ---------------------------------------------

-32

-116 plus or minus 141.1

= -----------------------------------

-32

= -25.1/(-32) (discard) and t = -116 - 141.1

------------------

-32

t = 8.03.

The rocket will hit the ground 8.03 seconds after it is launched.