Question

HELP! THIS IS ALGEBRA 1 HW!
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 + h ( with a bottom exponent of 0). Let h(t) = 0

b) Use the quadratic formula to 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

a) After substitution, formula looks like this:
\[h=-16t^2+116t+101\] When you let h(t) = 0, it looks something like this:\[0=-16t^2+116t+101\]b) Use the quadratic formula to factor and get the values for t:\[t=\frac{ -(116)\pm \sqrt{(116)^2-4(-16)(101)} }{ -32 }\rightarrow t=\frac{ -116\pm \sqrt{19920} }{ -32 }\]\[t \approx 3.7,-3.7\] Since we know time can't be negative, the only acceptable value of t here is then -3.7.

Therefore, the rocket will take approximately 3.7 seconds to hit the ground after it's launched.

Answer 2

Sorry in the statement where it says: "Since we know time can't be negative....", change -3.7 to +3.7. I mean to say that the only acceptable value of t here is then 3.7 because time can't be negative but accidentally typed up -3.7. Sorry about that.

Answer 3

I got 8 secs

Answer 4

I didn't use the quadratic formula for this. I substituted everything in.