LAUNCH
u_x30.0 m/s
u_y40.0 m/s
u50.0 m/s
θ53°

SHOW
Projectile
Vertical ball
Horizontal ball

GRAVITY

ACTIONS
TIME
t

VELOCITIES
v (proj)
v_vert
v_horiz
t0.0 s

Two Motions, One Ball

When you launch a projectile, it does two things at the same time: it moves forward, and it falls. Neither one gets in the way of the other. Here you launch three balls together. One only moves up and down on a track. One only rolls forward along a rail. The third one is the projectile, doing both. Watch it stay right above the rolling ball and right beside the one going up, the whole way.

Controls

Set the launch with the u_x and u_y sliders, or with u and θ — all four are linked, so moving one updates the others. Show or hide any of the three balls. Switch gravity between 10 and 9.8. Press Launch to fire, then Play, Pause, or drag the time slider to any moment in the flight. Reset unlocks the sliders and puts everything back.

Variables and outputs

Once launched, dashed lines connect the projectile down to the rolling ball and across to the rising ball. Velocity arrows appear on all three. The arrow on the up-and-down ball shrinks to nothing at the top and then reverses. The arrow on the rolling ball never changes at all. The panel shows the time, the projectile's speed with its two components, and each companion ball's speed.

Model assumptions

No air resistance. Flat ground, launched from the ground.

Learning objective

You should be able to hide the projectile, look only at the other two balls, and point to where it would be.