Q1.
A cricket shot. Think of a cricket ball being hit for a six. You want to make a simple model. What details would you include? What would you ignore?
Answer
First fix the question the model has to answer: “Will the ball cross the boundary without hitting the ground first?” Everything the model keeps or drops is decided by that one question.
| Keep in the model | Why it is needed | Ignore |
|---|---|---|
| Mass of the ball | Fixes how much the bat's blow speeds it up | Brand of the bat |
| Speed just after the hit (u) | Range grows as u² | Colour of the ball |
| Direction (angle) of the hit | Decides how the speed is shared between height and distance | Amount of grass on the field |
| Height of the bat above ground | Small, but it adds a little to the range | Stitching of the seam |
| Distance to the boundary | The number the answer is compared with | Spin of the ball |
With those few quantities the ball can be treated as a point moving under gravity alone. For a hit at u = 30 m s⁻¹ at 45°:
range R = u² sin 2θ / g
R = (30 m s⁻¹)² × sin 90° / (9.8 m s⁻²)
R = 900 m² s⁻² / 9.8 m s⁻²
R = about 92 m — comfortably past a 70 m boundary
R = (30 m s⁻¹)² × sin 90° / (9.8 m s⁻²)
R = 900 m² s⁻² / 9.8 m s⁻²
R = about 92 m — comfortably past a 70 m boundary
Why it happens: a model is not judged by how much of the real world it contains, but by whether it answers the question. The colour of the ball cannot enter any equation that links speed, angle and distance, so keeping it would add work without adding accuracy. Air resistance, spin and the seam do have real effects — they can shorten a big hit by ten metres or more — but they are small compared with the effect of u and θ, so a first model leaves them out. As the model is made more complex, these details are added back for greater accuracy.
Check it yourself: put u = 25 m s⁻¹ into the same formula. R = 625/9.8 ≈ 64 m — now the ball lands inside a 70 m boundary. A drop of only 5 m s⁻¹ in bat speed turns a six into a catch, which is exactly why the model keeps u and drops the bat's brand.