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A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20

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Question: A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)

Options:

  1. 2 s
  2. 3 s
  3. 4 s
  4. 5 s

Correct Answer: 3 s

Solution: 

Using the equation of motion: h = ut + 0.5gt². 20 = 5t + 0.5 * 10 * t². This simplifies to 5t + 5t² - 20 = 0. Solving gives t = 2 s.

A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20

Practice Questions

Q1
A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)
  1. 2 s
  2. 3 s
  3. 4 s
  4. 5 s

Questions & Step-by-Step Solutions

A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)
Correct Answer: 2 seconds
  • Step 1: Identify the variables in the problem. We have initial height (h) = 20 m, initial velocity (u) = 5 m/s, and acceleration due to gravity (g) = 10 m/s².
  • Step 2: Write down the equation of motion that relates height, initial velocity, time, and acceleration: h = ut + 0.5gt².
  • Step 3: Substitute the known values into the equation: 20 = 5t + 0.5 * 10 * t².
  • Step 4: Simplify the equation: 20 = 5t + 5t².
  • Step 5: Rearrange the equation to set it to zero: 5t² + 5t - 20 = 0.
  • Step 6: Divide the entire equation by 5 to make it simpler: t² + t - 4 = 0.
  • Step 7: Use the quadratic formula to solve for t: t = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = 1, c = -4.
  • Step 8: Calculate the discriminant: b² - 4ac = 1² - 4*1*(-4) = 1 + 16 = 17.
  • Step 9: Substitute the values into the quadratic formula: t = (-1 ± √17) / 2.
  • Step 10: Calculate the two possible values for t. Since time cannot be negative, we take the positive value: t ≈ 2 seconds.
  • Equations of Motion – The question tests the understanding of the equations of motion, particularly how to apply them to calculate the time of flight for an object under constant acceleration.
  • Initial Velocity and Acceleration – It assesses the ability to incorporate initial velocity and gravitational acceleration into the motion equations.
  • Quadratic Equations – The problem requires solving a quadratic equation, which is a key skill in physics problems involving motion.
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