Q.Read the following passage and answer the questions that follow. At the school athletics meet, Karan competes in the shot put and Ravi in the javelin. Karan's coach tells him to release the shot at about 40° and from as high a point as he can reach, and reminds him that increasing his release speed matters more than anything else. Ravi's coach tells him to release the javelin at about 32°, and warns him that the wind will affect his throw far more than it affects Karan's.

(i) Projectile. A projectile is any body that is thrown, hit, kicked or projected into the air and then travels freely under the influence of gravity and air resistance alone, receiving no further propulsive force after release (a shot, a javelin, a football, a long jumper's body). The five factors that affect its trajectory are:

1. Angle of projection (release)
2. Speed / velocity of projection (release)
3. Height of projection (release)
4. Gravity
5. Air resistance (with spin as a further influence)

(ii) Why about 40°, not 45°. The 45^° optimum comes from R = v^2sin(2θ)/g, which is derived only for a projectile that lands at the same height from which it was launched. Karan releases the shot from about shoulder height, well above the ground on which it lands. That extra height gives him extra flight time for free, so less of his release velocity needs to be spent going upward and more can be spent going forward. The optimum angle therefore falls below 45^° — around 40^°.

(iii) Percentage increase in range.

1. R₂/R₁ = (12/10)² = (1.2)² = 1.44
2. Increase = 1.44 - 1 = 0.44
3. Percentage increase = 0.44 × 100 = 44%

A 20 % rise in release speed yields a 44 % rise in range — because range depends on v squared, gains in speed are magnified, while angle and height give only modest returns. That is why release speed is the most important factor. …

(i) Define a projectile and name the five factors affecting its trajectory

Definition

A projectile is any body that is thrown, struck, kicked or otherwise projected into the air, and which thereafter travels freely through the air under the influence of gravity and air resistance alone — no propelling force acts on it once it has left the hand, foot or implement.

In sport, projectiles include the shot, discus, javelin and hammer, a football, cricket ball or basketball in flight, and even the athlete's own body during a long jump, high jump or gymnastic vault.

Its path through the air is called its trajectory. For a body affected only by gravity, that path is a parabola; air resistance distorts the parabola, sometimes severely.

The five factors

Spin is a further influence: it can generate lift, produce swerve (the Magnus effect) and stabilise an implement in flight.

(ii) Why Karan is coached to about 40°, not 45°

The 45^° result is not wrong — it is conditional. Look again at the formula. R is maximum when sin(2θ) = 1, i.e. 2θ = 90^°, i.e. θ = 45^°. But that derivation assumes the projectile lands at exactly the height from which it was launched.

In the shot put the condition is plainly broken:

• Karan releases the shot from full arm extension above the shoulder — roughly two metres above the circle.
• The shot lands on the ground, at height zero.

So the shot is released above its landing surface. Two consequences follow, and they are the biomechanical reason:

1. Flight time is partly free. Because the shot starts high, gravity has an extra couple of metres to work through before it lands. It stays airborne longer than a level-to-level throw at the same angle would.
2. Horizontal velocity therefore becomes the better investment. In a level throw, the only way to buy flight time is to send the shot upward — so half the effort must go into height. Here, some of the flight time has already been paid for by the release height, so it pays to put more of the release speed into the horizontal direction and less into the vertical. And "more horizontal, less vertical" means a lower angle.

Hence the optimum angle falls below 45^°. The higher the release point relative to the distance thrown, the further below 45^° it falls — which is why coaches teach roughly 36°–40° for the shot put. This is also why Karan is told to release from as high a point as he can reach: the height itself adds distance and it is what makes the lower angle correct.

Ravi's javelin sits lower still (about 32^°) because, on top of the release-height effect, the javelin is aerodynamic — it glides, and a flatter release angle exploits that glide.

(iii) The effect of raising release speed from 10 m/s to 12 m/s

Working:

1. Form the speed ratio:

   v₂/v₁ = (12 m/s)/(10 m/s) = 1.2

   (a 20 % increase in release speed)

2. Square it, because range varies as the square of speed:

   R₂/R₁ = (1.2)² = 1.44

3. So the new range is 1.44 times the old range:

   R₂ = 1.44 R₁

4. Find the increase:

   (R₂ - R₁)/R₁ = 1.44 - 1 = 0.44

5. Convert to a percentage:

   Percentage increase = 0.44 × 100 = 44 %

Sanity check with a concrete number: if Karan had been throwing 12 m, his new range is 1.44 × 12 = 17.28 m — an increase of 5.28 m, and 5.28 / 12 = 0.44 = 44%. ✓

Why release speed is called the most important factor

Compare what each factor returns:

The squared term is the whole story. A 20 % improvement in speed does not give 20 % more distance — it gives 44 % more. Doubling the release speed would quadruple the range (2² = 4). No other factor multiplies its benefit like this, and no other factor can be improved as much by training. Angle can be optimised once and then it is done; height is essentially given by the athlete's body. Speed can go on being trained — through strength, power and rate-of-force-development work. That is why every throws coach makes release velocity the priority.

(iv) Why air resistance matters far more to the javelin than to the shot

Air resistance (drag) grows with the surface area presented to the air and with the square of the speed; but whether that force matters depends on how it compares with the implement's weight. So the decisive property is the ratio of surface area to mass — in effect, the implement's density and shape.

Putting it together: …