Colliding projectiles

Two projectiles collide when their positions coincide — write both, equate, solve for t.

Colliding projectiles0 min · Free lecture

In this lesson

  • Two projectiles collide when their positions coincide — write both, equate, solve for t.

Collision is a position equation, not a velocity one.

For projectiles launched at different angles/speeds from possibly different points, equate x₁ = x₂ and y₁ = y₂. The same t must satisfy both.

If the question gives 'they collide mid-air', you have two equations and the unknowns usually close.

x1(t)=x2(t),y1(t)=y2(t)x_1(t)=x_2(t),\quad y_1(t)=y_2(t)

Collision conditions

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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Colliding projectiles — FemtoLearn.
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Two projectiles collide when their positions coincide — write both, equate, solve for t.
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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°