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Kinematics

Projectiles launched at an angle

  • 2 things to know
  • AS Unit 1

Overview

Recall questions on Projectiles launched at an angle.

What you need to know

Answer each one before you reveal it.

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Key term

Why is the speed of a projectile not zero at the highest point of its path?

Key term

Why does a projectile launched over level ground take the same time to rise as it does to fall?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    A ball is launched at 24 m s⁻¹ at 30° above the horizontal. Calculate the horizontal and vertical components of its initial velocity.

    Model answer

    The horizontal component is 24 cos 30° = 20.8 m s⁻¹ and the vertical component is 24 sin 30° = 12.0 m s⁻¹ upwards.

  2. 2

    A ball is kicked at 18 m s⁻¹ at 55° above the horizontal. Calculate the time it takes to reach its highest point, taking g as 9.81 m s⁻².

    Model answer

    The vertical component of the launch velocity is 18 sin 55° = 14.7 m s⁻¹, and this falls to zero in 14.7 ÷ 9.81 = 1.50 s.

  3. 3

    An arrow is shot at 40 m s⁻¹ at 25° above the horizontal. Calculate the greatest height it reaches above its launch point, taking g as 9.81 m s⁻².

    Model answer

    The vertical component of the launch velocity is 40 sin 25° = 16.9 m s⁻¹, and the rise is 16.9² ÷ (2 × 9.81) = 14.6 m.

  4. 4

    A stone is thrown at 15 m s⁻¹ at 40° above the horizontal over level ground. Calculate its total time of flight, taking g as 9.81 m s⁻².

    Model answer

    The vertical component of the launch velocity is 15 sin 40° = 9.64 m s⁻¹, and the flight lasts 2 × 9.64 ÷ 9.81 = 1.97 s.

  5. 5

    A ball is struck at 22 m s⁻¹ at 35° above the horizontal over level ground. Calculate its horizontal range, taking g as 9.81 m s⁻².

    Model answer

    The horizontal component is 22 cos 35° = 18.0 m s⁻¹ and the flight lasts 2 × 22 sin 35° ÷ 9.81 = 2.57 s, so the range is 46.4 m.

  6. 6

    Why is the speed of a projectile not zero at the highest point of its path?

    Model answer

    Only the vertical component of the velocity is zero there. The horizontal component is unchanged from launch, and it is that component which gives the projectile its speed at the top.

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