A batsman deflects a ball through 90° without changing its initial speed, which is 54 km h⁻¹. The mass of the ball is 0.5 kg. Find the magnitude of the impulse imparted to the ball in N s.
Physics · Mixed Chapter
JEE Main Practice

Question

A batsman deflects a ball through 90° without changing its initial speed, which is 54 km h⁻¹. The mass of the ball is 0.5 kg. Find the magnitude of the impulse imparted to the ball in N s.

G1 Physics · Accepted Answer

Step 1: Convert speed: v = 54 × 5/18 = 15 m s⁻¹. Step 2: Initial and final velocity vectors have the same magnitude v, with 90° between them. Step 3: Magnitude of velocity change |Δv⃗| = √(v² + v² − 2v² cos 90°) = v√2. Step 4: Impulse J = m|Δv⃗| = 0.5 × 15 × √2 = 7.5√2 ≈ 10.6066 N s. Final answer: 10.6 N s.