An interactive introduction to MATLAB

C.5loops 91

Flight of a model rocket
The rocket is assumed to be a particle that moves along a straight line in
the vertical plane. For motion with constant acceleration along a straight
line, the velocity and position as a function of time are given by:

v(t) =v 0 +at and s(t) =s 0 +v 0 t+^1

2

at,

wherev 0 ands 0 are the initial velocity and position, respectively. The
flight of the rocket can be divided into three segments and you should
calculate each segment using a separatewhileloop in your script.

Segment 1 - The first 0.15 s when the rocket engine is on
During this period, the rocket moves up with a constant acceleration. The
acceleration is determined by drawing a free body and a mass acceleration
diagram. From Newton’s second law, summing the forces in the vertical
direction gives an equation for the acceleration:

a=

FE−mg

m

The velocity and height as a function of time are:

v(t) = 0 +at and h(t) = 0 + 0 +

1

2 at

(^2) ,
where the initial velocity and initial position are both zero. In your script
thiswhileloop starts att= 0 and continues looping as long ast 6 0.15 s.
The time, velocity and height at the end of this segment aret 1 ,v 1 , andh 1.
Segment 2 - The motion from when the engines stops until the parachute
opens
In this segment the rocket moves with a constant decelerationg. The
speed and height of the rocket as a function of time are given by:
v(t) =v 1 −g(t−t 1 ) and h(t) =h 1 +v 1 (t−t 1 ) −

1

2 g(t−t^1 )

2

In your script thiswhileloop should continue looping until the velocity
of the rocket is−20 m/s(negative since the rocket is falling). The time
and height at the end of this segment aret 2 andh 2.