A ball is thrown downwards at 8.3 m s-1 from the top of a building. After 1.2 seconds accelerating at 9.81 m s-2, what is its speed? Give your answer to two decimal places.

Question

BlackTom AI · Accepted Answer

Use the constant-acceleration kinematic relation v = u + at. Here u is the initial speed, a is the acceleration, t is the time, and v is the final speed.

Relevant knowledge points:
- For motion with constant acceleration, velocity changes linearly with time: v = u + at.
- Keep a consistent sign convention. The ball is thrown downwards and accelerates downwards, so using positive magnitudes for both is appropriate when asking for speed (magnitude of velocity).
- Report the final answer with correct units and rounding.

Step-by-step reasoning and calculations:
1. Identify values: u = 8.3 m s^-1, a = 9.81 m s^-2, t = 1.2 s.
2. Apply the formula: v = u + a t.
3. Compute the product a t: 9.81 × 1.2 = 9.81 × (12/10) = (9.81 × 12) / 10.
   - 9.81 × 12 = 9.81 × (10 + 2) = 98.1 + 19.62 = 117.72.
   - Divide by 10: 117.72 / 10 = 11.772 m s^-1.
4. Add to the initial speed: v = 8.3 + 11.772 = 20.072 m s^-1.
5. Round to two decimal places: 20.072 → 20.07 m s^-1 (the third decimal digit is 2, so we round down).

Why this answer is correct:
- The kinematic equation directly gives the final velocity under constant acceleration. The arithmetic yields 20.072 m s^-1, and proper rounding to two decimal places gives 20.07 m s^-1. Units are consistent throughout.

Common incorrect approaches (brief):
- Using g = 10 m s^-2 would give a different numeric result (8.3 + 10×1.2 = 20.3), which is less precise.
- Confusing displacement formulas (like s = ut + 1/2 at^2) with the velocity formula would lead to wrong computations.
- Incorrect sign convention could produce a negative value if direction is treated inconsistently.

Conclusion: The final speed after 1.2 s is 20.07 m s^-1, which matches the provided answer.

A ball is thrown downwards at 8.3 m s-1 from the top of a building. After 1.2 seconds accelerating at 9.81 m s-2, what is its speed? Give your answer to two decimal places.Numerical

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