Question

You make a 2 kg model rocket and watch it reach a maximum height of 41 m. The work done by air-resistance is -161 J. In the first answer box, enter the initial speed of the rocket and in the second answer box, enter how high the rocket would have reached if there were no air-resistance.

Answer 1

(1) Maximum altitude = 2.51 m
(2) Travel time to maximum altitude = 11.2 s

Here's how it's done....

m = 2 kg

let

F = 10 N

t = 1.0 s
Vi = 0.0 m/s

First the acceleration portion of the problem -- find acceleration from thrust

F = MA.... so... A = F/M

A = (10 N) / (2 kg)
A = 5 m/s^2

Find the final velocity at engine cut-out

Vf = (t * A) + Vi

Vf = [ (1.0 s) * (5 m/s^2) ]
Vf = 5 m/s

Find the distance covered during the launch

d = 1/2 ( Vf + Vi ) × t

d = 0.5 * [ (5 m/s) + (0.0 m/s) ] * (1.0 s)
d = 2.5 m

Now Vf = Vo for the trajectory portion of the problem

Vo = 5 m/s
θ° = 90
Yo = 2.5 m
g = 9.80665 m/s^2



Tr = Vo/g
Tr = (5 m/s) / (9.80665 m/s^2)
Tr = 0.51 s

Find that maximum altitude

H = Yo + Vo*Tr - 0.5*g*Tr^2
H = (2.5 m) + [ (5 m/s) * (.51s) ] - [ 0.5 * (9.80665 m/s^2) * (.51 s)^2 ]
H =2.551


Total time is the length of time before engine cut-off plus after cut-off

Tt = Te + Tr
Tt = (1.0 s) + (.51 s)
Tt = 1.51s