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NEET PHYSICSMedium

A car starts from rest and accelerates at 5 m/s25\text{ m/s}^2. At t=4 st = 4\text{ s}, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6 st = 6\text{ s}? (Take g=10 m/s2g = 10\text{ m/s}^2)

A

20 m/s20\text{ m/s}, 5 m/s25\text{ m/s}^2

B

20 m/s20\text{ m/s}, 00

C

202 m/s20\sqrt{2}\text{ m/s}, 00

D

202 m/s20\sqrt{2}\text{ m/s}, 10 m/s210\text{ m/s}^2

Step-by-Step Solution

Initial velocity of car = 00. Acceleration of car = 5 m/s25\text{ m/s}^2. Velocity of car at t=4 st = 4\text{ s}; v=u+atv=0+5×4=20 ms1v = u + at \Rightarrow v = 0 + 5 \times 4 = 20\text{ ms}^{-1}. At t=4 st = 4\text{ s}, a ball is dropped out of a window so velocity of ball at this instant is 20 ms120\text{ ms}^{-1} along horizontal. After 2 seconds of motion: Horizontal velocity of ball = 20 ms120\text{ ms}^{-1} (ax=0\because a_x = 0). Vertical velocity of ball (vyv_y) = uy+ayt=0+10×2=20 ms1u_y + a_yt = 0 + 10 \times 2 = 20\text{ ms}^{-1} (ay=g=10 m/s2\because a_y = g = 10\text{ m/s}^2). So magnitude of velocity of ball v=vx2+vy2=202 m/sv = \sqrt{v_x^2 + v_y^2} = 20\sqrt{2}\text{ m/s}. Acceleration of ball at t=6 st = 6\text{ s} is g=10 m/s2g = 10\text{ m/s}^2 as ball is under free fall.

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