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Projectile motion

Reach the target by changing the angle and speed. Also look for the conditions that will take you the furthest.

    P02 · Angle and velocity components0.00 s · Ready
    A scene where a ball travels parabolically on a launch pad and lands near the target.

    Physics/Mechanics/Principles and Exploration

    Projectile motion — principles and investigation

    The thrown ball moves forward and falls down at the same time. In the parabolic launcher, the launch angle, initial speed, and launch height are changed and the range, peak point, and flight time are compared. By dividing horizontal and vertical motions, we can describe multiple trajectories reaching the same target.

    How does it work?

    At the same height, R = v₀²sin(2θ)/g. It goes furthest at 45°.

    Key relationship

    x = v₀cosθ · t · y = h + v₀sinθ · t − ½gt²

    Try this investigation

    1. Fire it and look at the trajectory and horizontal and vertical speed arrows. The target is moved with a flag or slider.
    2. Set the speed to 20 m/s and the height to 0 m. Run and record at angles of 30°, 45°, and 60°, respectively.
    3. Leave the speed the same and increase the launch height to 10 m. Compare the ranges of 35° and 45°.

    Interpreting your results

    What is the range of 30° and 60° when the speed is the same at the same height?

    At R = v₀²sin(2θ)/g, sin 60° and sin 120° are the same.

    Assumptions and limitations

    Gravity is constant at 9.8 m/s² and ignores air resistance, size and rotation of the ball. As you increase the height, the optimal angle becomes less than 45°. The target only determines the horizontal position of the floor.