Question

A rocket is launched from atop a 55-foot cliff with an initial velocity of 138 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.

Answer 1

It would take 9 seconds.

Substituting the values into the equation, we have:

0 = -16t² + 138t + 55

The quadratic formula is:

`t=(-b\pm √(b^2-4ac))/(2a)`

Inserting our information we have:

`t=(-138\pm √(138^2-4(-16)(55)))/(2(-16)) \\ \\=(-138\pm √(19044--3520))/(-32) \\ \\=(-138\pm √(19044+3520))/(-32) \\ \\=(-138\pm √(22564))/(-32) \\ \\=(-138\pm 150)/(-32)=(-138+150)/(-32)\text{ or } (-138-150)/(-32) \\ \\=(12)/(-32)\text { or } (288)/(32)=-0.375 \text{ or } 9`