Rocket at an Angle

ΔtSpeed

Thrust30 Nweight 50 N

Thrust direction0°from +x

FieldMass

Start velocity0 m/s

sizedirection

Velocity along the path

Forces on the rocket

Drag the rocket to start it from anywhere in the picture.

Clock reading: t = 0.00 s
Position: (0.0, 100.0) m
Velocity: 0.0 m/s

1×

\vec{F}_{\text{net}}

=

\vec{F}_{\text{thrust}}

+

\vec{F}_g

58.3 N

30 N

50 N

Two forces act on the rocket: the thrust, the push of the hot exhaust gas on it, and $\vec{F}_g$ , the planet's pull, of size $mg$ . Put the tail of $\vec{F}_g$ on the tip of $\vec{F}_{\text{thrust}}$ . The net force runs from the first tail to the last tip.

Keys

The keys work while the simulation is selected: click anywhere on it first.

↑ ↓: 5 N more or less thrust
← →: Turn the thrust 5° counterclockwise or clockwise
Space: Play or pause
S: Run one step, or the next link of the chain
R: Reset
− =: Zoom the picture out or in
1 to 4: Show the forces, the second law, the velocity or the equations

How the simulation works

The simulation holds the net force constant during each time step $\Delta t$ . The acceleration is then constant through the step, so the velocity changes as EOM #1 says, $\vec{v}_f = \vec{a}\,\Delta t + \vec{v}_i$ , and the position changes as EOM #2 says, along $x$ and along $y$ . A change to the thrust takes effect at once: the time step ends at that instant, and the next one starts with the new force. The rocket's mass stays the same through the flight, as if it burned no fuel, and there is no air resistance.

A flight ends when the rocket reaches the ground. Otherwise it runs until you press Pause or Reset, with no time limit. Changing the field, the mass or the start velocity starts the flight again from the beginning.

The simulation flies a rocket that starts $100\;\text{m}$ above the ground. Two forces act on it: the thrust, which you set, and the pull of the planet. It flies one time step $\Delta t$ at a time, and holds the net force constant during each step, so the motion in each step follows the equations of motion exactly.

The panel beside the flight shows one link of the chain at a time. Forces: the thrust and the planet's pull, added tip to tail, make the net force. Second law: the net force multiplied by $\dfrac{1}{m}$ is the acceleration. Velocity: the acceleration multiplied by $\Delta t$ is the change in velocity, $\Delta\vec{v}$ , and adding $\Delta\vec{v}$ to the velocity at the start of the step gives the velocity at its end. Equations: all three, worked by components with units. Hide panel gives the picture of the flight the panel's width as well.

Press Step to work one step the way you would on paper: the forces, then the second law, then the velocity, as the rocket moves along its path to the end of the step. Press Play to run step after step; at a speed of 0.1×, each second of flight takes ten seconds. While the simulation is selected, the arrow keys change the thrust as it flies: up and down for its size, left and right for its direction. A change takes effect at once. Drag the rocket to start it from anywhere in the picture, and choose which forces the picture draws on it: each force, the net force, or none.

The − and + buttons in the corner of the picture zoom it out and in. Zooming out shows more of the path and draws the rocket smaller. The arrows keep their lengths, because their scales are in newtons, in meters per second squared and in meters per second, not in meters.

Try each of these, and watch the panel as you do:

From rest: compare the direction of each $\vec{v}_f$ with the direction of $\vec{a}$ .
A start velocity straight up: watch which way each $\Delta\vec{v}$ points, and which way $\vec{v}_f$ turns from one step to the next.
Deep space, with no gravitational force: turn the thrust with the arrow keys, and watch $\vec{F}_{\text{net}}$ and $\vec{a}$ .
Net force on the rocket, and Play: steer with the arrow keys, and compare the direction of $\vec{F}_{\text{net}}$ with the direction the rocket moves.
A different mass with the same thrust: watch which arrows change and which stay the same.
A time step of $2\;\text{s}$ , then $0.25\;\text{s}$ : compare $\Delta\vec{v}$ with $\vec{a}$ in the panel, and the path each one draws.