A ball of mass 2 kg is thrown up with a velocity of 20 m. Class 9

A ball of mass 2 kg is thrown up with a velocity of 20 m. Class 9

Question 1.

A ball of mass 2 kg is thrown up with a velocity of 20 m s^-1. Class 9

(i) Identify the sign of the work done by gravity on the ball during its upward motion and its downward motion.

(ii) If the ball reaches a height of 19.4 m, how much work was done by air resistance (assume g = 10 m s^-2).

Answer:

(i) Upward motion: Gravity acts downward, displacement is upward - opposite directions → work done by gravity = negative. Downward motion: Gravity and displacement both act downward - same direction →work done by gravity = positive.

(ii) Initial KE = 1/2 × 2 × (20)² = 400 J. Without air resistance: h = v²/(2g) = 400/20 = 20 m (ball would reach 20 m). Actual height = 19.4 m. PE at 19.4 m = mgh = 2 × 10 × 19.4 = 388 J. At highest point, final KE = 0. By work- energy theorem: Work by gravity + Work by air resistance = ∆KE = 0 - 400 = - 400 J. Work by gravity = - mgh = -388 J. Work by air resistance = - 400 - (- 388) = -12 J.