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A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m.

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

Options:

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

Correct Answer: 4 s

Solution: 

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

A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m.

Practice Questions

Q1
A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m. How long will it take to hit the ground? (Assume 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 downward with an initial speed of 10 m/s from a height of 20 m. How long will it take to hit the ground? (Assume g = 10 m/s²)
Correct Answer: 2 seconds
  • Step 1: Identify the variables in the problem. The initial speed (u) is 10 m/s, the height (h) is 20 m, and the acceleration due to gravity (g) is 10 m/s².
  • Step 2: Write down the equation of motion that relates height, initial speed, time, and acceleration: h = ut + 0.5gt².
  • Step 3: Substitute the known values into the equation: 20 = 10t + 0.5 * 10 * t².
  • Step 4: Simplify the equation: 20 = 10t + 5t².
  • Step 5: Rearrange the equation to set it to zero: 5t² + 10t - 20 = 0.
  • Step 6: Use the quadratic formula or factor the equation to find the value of t. The quadratic formula is t = (-b ± √(b² - 4ac)) / 2a.
  • Step 7: In this case, a = 5, b = 10, and c = -20. Calculate the discriminant: b² - 4ac = 10² - 4 * 5 * (-20) = 100 + 400 = 500.
  • Step 8: Calculate t using the quadratic formula: t = (-10 ± √500) / (2 * 5). Since we are looking for a positive time, we take the positive root.
  • Step 9: Simplify to find t = 2 seconds.
  • Kinematics – The question tests the understanding of the equations of motion, specifically how to apply them to calculate the time of flight for an object under constant acceleration.
  • Quadratic Equations – The problem requires solving a quadratic equation, which is a key skill in physics and mathematics.
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