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NEET PHYSICSMedium

A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 s another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v? (take g = 10 ms⁻²)

A

75 ms⁻¹

B

55 ms⁻¹

C

40 ms⁻¹

D

60 ms⁻¹

Step-by-Step Solution

  1. Motion of the First Ball (Dropped): Initial velocity u1=0u_1 = 0. Time taken to meet t1=18t_1 = 18 s. Acceleration a=g=10a = g = 10 ms⁻². Using the kinematic equation for displacement h=ut+12gt2h = ut + \frac{1}{2}gt^2 : h=0×18+12×10×(18)2h = 0 \times 18 + \frac{1}{2} \times 10 \times (18)^2 h=5×324=1620 mh = 5 \times 324 = 1620 \text{ m}

  2. Motion of the Second Ball (Thrown): It is thrown 6 seconds later, so its time of flight is t2=186=12t_2 = 18 - 6 = 12 s. Initial velocity u2=vu_2 = v. It covers the same distance h=1620h = 1620 m. Applying the displacement equation: 1620=v(12)+12×10×(12)21620 = v(12) + \frac{1}{2} \times 10 \times (12)^2 1620=12v+5×1441620 = 12v + 5 \times 144 1620=12v+7201620 = 12v + 720 12v=1620720=90012v = 1620 - 720 = 900 v=90012=75 ms1v = \frac{900}{12} = 75 \text{ ms}^{-1}

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