Projectiles Launched at an Angle · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Launching at an angle

Science · Forces & Motion · ages 16-18
Name ______________________   Date ____________

  1. A ball is kicked at 20 m/s, 30 degrees above horizontal. What is its initial upward velocity in metres per second?

    Answer: ______________

  2. A ball launches at 24 m/s, 60 degrees above horizontal. Use cos(60 degrees) = 0.5. What is its initial horizontal velocity?

    • 12 m/s
    • 20.8 m/s
    • 24 m/s

  3. A ball is in flight with gravity as the only force acting on it. What is its horizontal acceleration?

    • 9.8 metres per second squared down
    • Zero
    • 9.8 metres per second squared up

  4. A ball has initial components 17 m/s horizontal and 9.8 m/s upward. It lands at launch height. With no air resistance and constant g = 9.8 m/s^2, what is its range in metres?

    Answer: ______________

  5. A ball launches at 19.6 m/s, 30 degrees above horizontal, and lands at launch height. Ignore air resistance and use constant g = 9.8 m/s^2. What is its total flight time in seconds?

    Answer: ______________

  6. A ball starts with an upward velocity of 9.8 m/s. Ignore air resistance and use constant g = 9.8 m/s^2. What is its greatest height above its launch point?

    • 2 m
    • 9.8 m
    • 4.9 m

  7. A ball launches from a fixed cliff top onto horizontal ground below. Hold launch speed fixed, assume constant downward gravity and ignore air resistance. How does the angle for greatest range compare with 45 degrees?

    • It stays at 45 degrees because landing height cannot change the best angle.
    • It is below 45 degrees because the extra drop shifts the best balance toward horizontal velocity.
    • It is above 45 degrees because the extra drop makes upward velocity more useful than horizontal velocity.

  8. A ball returns to launch height. Hold launch speed fixed, assume constant downward gravity and ignore air resistance. Which angle above horizontal gives greatest range, and why?

    • 45 degrees: equal components maximize their product at fixed speed
    • 60 degrees: the longer flight always outweighs the smaller horizontal component
    • 30 degrees: the larger horizontal component always outweighs the shorter flight
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Answer key

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Launching at an angle W1-mt_MMuacyCqb8-s1

  1. 10 · The upward component is u sin(theta): 20 times sin(30 degrees) = 20 times 0.5 = 10 m/s.
  2. 12 m/s · The horizontal component uses cosine when the angle is measured above horizontal: 24 times 0.5 = 12 m/s.
  3. Zero · Gravity acts vertically. With no horizontal force, horizontal acceleration is zero.
  4. 34 · Climb time is 1 s and total flight time is 2 s. Horizontal velocity stays at 17 m/s, so range is 17 times 2 = 34 m.
  5. 2 · The upward component is 9.8 m/s, so the climb takes 1 s. Landing at launch height adds an equal fall time, giving 2 s.
  6. 4.9 m · At the top, vertical velocity is zero. The rise is u_y squared/(2g) = 96.04/19.6 = 4.9 m.
  7. It is below 45 degrees because the extra drop shifts the best balance toward horizontal velocity. · The lower ground adds flight time. At fixed speed and cliff height, the greatest range occurs below 45 degrees, with more horizontal velocity than a 45-degree launch.
  8. 45 degrees: equal components maximize their product at fixed speed · Equal-height range is 2u_x u_y/g. At fixed speed, the component product is greatest when u_x = u_y, which occurs at 45 degrees above horizontal.
Worksheet · LightMySky