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A ball is thrown vertically downwards with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with the velocity of 80 m/s. The height of the tower is: (assuming g = 10 m/s²)

A

340 m

B

320 m

C

300 m

D

360 m

Step-by-Step Solution

  1. Identify Given Values: Initial velocity, u=20 m/su = 20 \text{ m/s} (directed downwards). Final velocity, v=80 m/sv = 80 \text{ m/s} (directed downwards). Acceleration, a=g=10 m/s2a = g = 10 \text{ m/s}^2 (directed downwards). Displacement, s=hs = h (height of the tower).

  2. Select Kinematic Equation: Use the equation relating velocities, acceleration, and displacement for uniformly accelerated motion : v2=u2+2asv^2 = u^2 + 2as

  3. Substitute and Solve: (80)2=(20)2+2(10)h(80)^2 = (20)^2 + 2(10)h 6400=400+20h6400 = 400 + 20h 20h=640040020h = 6400 - 400 20h=600020h = 6000 h=600020=300 mh = \frac{6000}{20} = 300 \text{ m}

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