Mathwizurd.com is created by David Witten, a mathematics and computer science student at Vanderbilt University. For more information, see the "About" page.

Apr 29 Rocket Ship

Joshua loves rockets. He has a toy rocket and he wants to predict how high it goes. If it weighs 2 kilograms, and exerts 40 Newtons of force for 10 seconds, how high up does the rocket go?

The first thing we need to calculate is the net acceleration of the rocket,  and since there gravity acts against it, we must take that into account when calculating the path of the rocket.

Fnet = ma
Rocket_Force - Fg = ma
40 - 9.8(2) = 2a
20.4 = 2a
a = 10.2 m/s^2

Now, this lasts for 10 seconds.

Vf = Vo + at
Vf = 0 + (10.2)(10)
Vf = 102 m/s

So, when the engine shuts off, it'll be going 102 m/s up. It's also important to find the distance travelled at that point.

d = VoT + 1/2aT^2
d = 0(T) + 5.1(100)
d = 510 m

At that point, the acceleration will be -9.8 m/s^2, and we know the final velocity is zero.

Vf^2 = Vo^2 + 2ad
0 = 102^2 + -19.8d
19.8d = 10404
d = 525.4545

Now, we add the distance when the engine is on and when the engine isn't.

d = 510 + 525.4545
d = 1035.4545 m

So, the rocket goes up 1035.4545 meters.

David Witten