Physics 101 Question I need help with?

a) after its engines stop the acceleration goes from 3 m/s^2 to -9.8 m/s^2 because of gravity. It starts decelerating (or you could say accelerating towards the earth).

it's velocity will be,

v^2 = vi^2 + 2*a(d-di) where vi is initial velocity and d is distance and di is initial distance

so, v^2=46^2 + 2*3(130-0)

v = 53.8 m/s at the moment the engines stop

b) i'll use v^2 = Vi^2 + 2*a(d-di) using the moment the rocket shuts it's engines off as the initial v and d point. So, v will be velocity at highest point, which means v = 0.

-(Vi^2) = 2*a(d-di)

-(Vi^2)/(2*a) + di = d

-(53.8^2)/(2*(-9.8)) + 130 = 278 m is the maximum height reached.

c) d = di + 1/2*a*t^2, d = 0 cause i'll just get the time it takes the rocket to fall from highest point which is equivalent.

(-di/(1/2(a))^(1/2) = t

(-278/(0.5*(-9.8)))^(1/2) = 7.5 seconds

d) the rocket is in the air twice as long, so 15 seconds. This is ignoring the effect of drag from the air molecules.

on a side note, I could be wrong about this but it seems strange that the rocket has an initial velocity. I believe usually in cases of rockets the initial velocity is taken as 0. To say it has an initial velocity would be like driving in a car at 46 m/s then firing the rocket out the window in the direction your driving. Obviously that's a fairly unlikely scenario.

the rocket will continue up until the vertical speed is reduced by gravity

vertical distance till burn out:

H= v(0) t +.5 a t^2

130 = 46t + .5(3) t^2 solve for t(bo) for time at burn out

find velocity at burn out

V = V(0) + a t

v(bo) =46 + 3 t(bo)

b) What is the maximum height reached by the rocket?

max height occurs when velocity =0

V =V(bo) -.5(9.8)t

0= V(bo) -.5(9.8)t(m) solve for t(m)

max height = 130 + V(bo) t -.5(9.8) t^2 solve using t(m)

(c) How long after liftoff does the rocket reach its maximum height?

maximum height is reached when t = t(bo) +t(m)

How long is the rocket in the air?

time for rocket to fall

0 =( maxheight) -.5(9.8)t^2 solve for time for rocket to fall

total time = time to burnout + time to max height +time to fall