Relative projectile motion (one body)

From one projectile's frame, the other moves uniformly — straight lines, constant speeds.

Relative projectile motion (one body)0 min · Free lecture

In this lesson

  • From one projectile's frame, the other moves uniformly — straight lines, constant speeds.

Inside a projectile's frame, gravity disappears.

In the frame of a projectile, the other projectile has zero relative acceleration: its path is a straight line with constant relative velocity.

This turns 'will they collide?' into 'does the straight line pass through the target point?'.

a⃗rel=a⃗1−a⃗2=0\vec a_{rel} = \vec a_1 - \vec a_2 = 0

Zero relative acceleration

Worked example

For a fixed launch speed, the horizontal range of a projectile is maximum when the launch angle is:

  1. R = v0² sin 2θ / g
  2. R is maximum when sin 2θ = 1, i.e. 2θ = 90°, so θ = 45°

Answer: 45°

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Relative projectile motion (one body) — FemtoLearn.
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From one projectile's frame, the other moves uniformly — straight lines, constant speeds.
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Practice

Free · 4 questions with full solutions
  1. Q1 · Numerical · difficulty 2/5

    A projectile is launched with speed 15 m/s at an angle 70° above the horizontal. Taking g = 10 m/s², find its horizontal range.

    R=v02sin⁡2θgR = \frac{v_0^2 \sin 2\theta}{g}
  2. Q2 · Numerical · difficulty 2/5

    A projectile is launched with speed 15 m/s at an angle 25°. Taking g = 10 m/s², find its maximum height above the launch point.

    H=v02sin⁡2θ2gH = \frac{v_0^2 \sin^2\theta}{2g}
  3. Q3 · Numerical · difficulty 2/5

    A projectile is launched with speed 25 m/s at an angle 15°. Taking g = 9.8 m/s², find its total time of flight.

  4. Q4 · MCQ · difficulty 1/5

    For a fixed launch speed, the horizontal range of a projectile is maximum when the launch angle is:

    • 30°
    • 45°
    • 60°
    • 90°