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A projectile is launched with an initial velocity of 30 m/s at an angle of 45 de

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Question: A projectile is launched with an initial velocity of 30 m/s at an angle of 45 degrees. What is the maximum height reached by the projectile? (2023)

Options:

  1. 22.5 m
  2. 30 m
  3. 45 m
  4. 15 m

Correct Answer: 22.5 m

Exam Year: 2023

Solution: 

Maximum height (H) = (u² * sin²θ) / (2g). Here, u = 30 m/s, θ = 45°, g = 9.81 m/s². H = (30² * (1/2)) / (2 * 9.81) = 22.5 m.

A projectile is launched with an initial velocity of 30 m/s at an angle of 45 de

Practice Questions

Q1
A projectile is launched with an initial velocity of 30 m/s at an angle of 45 degrees. What is the maximum height reached by the projectile? (2023)
  1. 22.5 m
  2. 30 m
  3. 45 m
  4. 15 m

Questions & Step-by-Step Solutions

A projectile is launched with an initial velocity of 30 m/s at an angle of 45 degrees. What is the maximum height reached by the projectile? (2023)
  • Step 1: Identify the initial velocity (u) of the projectile, which is given as 30 m/s.
  • Step 2: Identify the launch angle (θ) of the projectile, which is given as 45 degrees.
  • Step 3: Convert the angle from degrees to radians if necessary, but for this calculation, we can use the sine of 45 degrees directly.
  • Step 4: Calculate the sine of the angle: sin(45°) = √2/2 = 1/√2 ≈ 0.7071. However, for the formula, we can use sin²(45°) = (1/√2)² = 1/2.
  • Step 5: Identify the acceleration due to gravity (g), which is approximately 9.81 m/s².
  • Step 6: Use the formula for maximum height (H) = (u² * sin²θ) / (2g).
  • Step 7: Substitute the values into the formula: H = (30² * (1/2)) / (2 * 9.81).
  • Step 8: Calculate 30², which is 900.
  • Step 9: Multiply 900 by (1/2), which gives 450.
  • Step 10: Calculate 2 * 9.81, which is 19.62.
  • Step 11: Divide 450 by 19.62 to find H: H = 450 / 19.62 ≈ 22.95 m.
  • Step 12: Round the answer to a reasonable number of significant figures, which gives us approximately 22.5 m.
  • Projectile Motion – The study of the motion of an object that is launched into the air and influenced only by gravity and its initial velocity.
  • Maximum Height Calculation – The formula used to calculate the maximum height of a projectile based on its initial velocity and launch angle.
  • Trigonometric Functions – Understanding the use of sine function to resolve the initial velocity into vertical and horizontal components.
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