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A projectile is launched at an angle of 30 degrees with an initial velocity of 2

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Question: A projectile is launched at an angle of 30 degrees with an initial velocity of 20 m/s. What is the maximum height reached by the projectile?

Options:

  1. 5 m
  2. 10 m
  3. 15 m
  4. 20 m

Correct Answer: 10 m

Solution: 

Maximum height (H) = (u^2 * sin^2(θ)) / (2g) = (20^2 * (1/2)^2) / (2 * 9.8) = 10.2 m.

A projectile is launched at an angle of 30 degrees with an initial velocity of 2

Practice Questions

Q1
A projectile is launched at an angle of 30 degrees with an initial velocity of 20 m/s. What is the maximum height reached by the projectile?
  1. 5 m
  2. 10 m
  3. 15 m
  4. 20 m

Questions & Step-by-Step Solutions

A projectile is launched at an angle of 30 degrees with an initial velocity of 20 m/s. What is the maximum height reached by the projectile?
Correct Answer: 10.2 m
  • Step 1: Identify the initial velocity (u) of the projectile, which is given as 20 m/s.
  • Step 2: Identify the angle of launch (θ), which is given as 30 degrees.
  • Step 3: Convert the angle from degrees to radians if necessary, but here we can use the sine function directly.
  • Step 4: Calculate the sine of the angle: sin(30 degrees) = 1/2.
  • Step 5: Use the formula for maximum height (H): H = (u^2 * sin^2(θ)) / (2g).
  • Step 6: Substitute the values into the formula: H = (20^2 * (1/2)^2) / (2 * 9.8).
  • Step 7: Calculate 20^2, which is 400.
  • Step 8: Calculate (1/2)^2, which is 1/4 or 0.25.
  • Step 9: Multiply 400 by 0.25 to get 100.
  • Step 10: Calculate 2 * 9.8, which is 19.6.
  • Step 11: Divide 100 by 19.6 to find the maximum height: 100 / 19.6 = 5.102 m.
  • Step 12: Round the answer to one decimal place, which gives us approximately 5.1 m.
  • Projectile Motion – The study of the motion of objects that are launched into the air and are subject to gravitational forces.
  • Kinematic Equations – Equations that describe the motion of objects, particularly in relation to velocity, acceleration, and displacement.
  • Trigonometry in Physics – Using trigonometric functions to resolve components of vectors, such as velocity in projectile motion.
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