Question

The ball initially has a velocity of 5 m/s in the positive x-direction and some time later has a velocity of 7 m/s in the positive y-direction. If the work done by the ball is 48 joule, then the mass of the ball in kg is:

• A. 2.5
• B. 6.5
• C. 4
• D. 2

Hint:

Use the work-energy theorem: Work done = change in kinetic energy, and remember that velocities in perpendicular directions can be treated using their magnitudes when calculating energy change.

Answer 1

The Correct Option is C

Step 1: Work-energy theorem.
W = ΔKE = ½ m v_f² - ½ m v_i².

Step 2: Speed magnitudes.
Initial speed v_i = 5 m/s along x; final speed v_f = 7 m/s along y.

Step 3: Substituting values.
48 = ½ m (7² - 5²) = ½ m (49 - 25) = ½ m · 24 = 12m.

Step 4: Solving for mass.
m = 48/12 = 4 kg.

Step 5: Conclusion.
The ball's mass is 4 kg.