The Cricket Reaction Puzzle – Time to React

We want to know how much time Sachin Tendulkar actually gets to react to a ball bowled by Shoaib Akhtar at 150 km/h over a distance of 20 m.

1. Convert speed to m/s

The given speed is in km/h, but the distance is in meters, so we convert to meters per second.

$$150\ \text{km/h} = 150 \times \frac{1000\ \text{m}}{3600\ \text{s}} = 150 \times \frac{10}{36} = 41.67\ \text{m/s}\ (\text{approximately})$$

2. Use the basic time–speed–distance relation

We use the formula:

$$\text{time} = \frac{\text{distance}}{\text{speed}}$$

Given:

• Distance $d = 20\ \text{m}$
• Speed $v = 41.67\ \text{m/s}$

So:

$$t = \frac{20}{41.67} \approx 0.48\ \text{s}$$

So Sachin has about 0.48 seconds (less than half a second) to see, decide, and play the shot.

3. What this visualization shows

This interactive visualization treats the ball as a point moving along a horizontal pitch from bowler to batter.

• The distance slider changes how far apart they are.
• The speed slider changes how fast the ball is bowled (in km/h).
• The slow-motion toggle lets you see the motion exaggerated in time.

On the screen you will see:

1. A horizontal "pitch" line from left (Shoaib) to right (Sachin).
2. A neon ball moving from bowler to batter.
3. A dynamic display of:
   • Current speed in m/s.
   • Time taken for the ball to reach the batter.
4. A faint vertical bar at the distance point showing where the batter stands.

Mathematically, we use:

$$v_{\text{m/s}} = v_{\text{km/h}} \cdot \frac{1000}{3600}$$ $$t_{\text{flight}} = \frac{d}{v_{\text{m/s}}}$$

We then map the real-time motion to animation time, looping every delivery so you can repeatedly see how little reaction time the batter gets.

For the puzzle values (150 km/h, 20 m) the visual will show about 0.48 s of flight time.