A rocket is launched from the top of a 40 foot cliff with an initial velocity of 160 feet per second. The​ height, h, of the rocket after t seconds is given by the equation h=-16+2+160+40. How long after the rocket is launched will it be 30 feet from the​ ground? t= feet or seconds

A rocket is launched from the top of a 40 foot cliff with an initial velocity of 160 feet per second. The height, h, of the rocket after t seconds is given by the equation h=-16+2+160+40. How long after the rocket is launched will it be 30 feet from the ground?

A rocket is launched from the top of a 40 foot cliff with an initial velocity of 160 feet per second. The height, h, of the rocket after t seconds is given by the equation h=-16+2+160+40. How long after the rocket is launched will it be 30 feet from the ground?t= 69 feet or seconds

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4