Question

A body sliding on a frictionless track which terminates in a straight horizontal section CD. The body starts slipping from A and reaches point D. If h1 = 1 m, then how far from point D, will the body hit the ground?Take, g = 10 ms-2.

• A. (A) 1 m
• B. (B) 2 m
• C. (C) 3 m
• D. (D) 4 m

Answer 1

Answer: (A)

(A) 1 m

Answer 2

Explanation:
Given:Height of point A, h1 = 1 mLet u be the speed of the body at point D.Total energy of the body at point A = Potential energy of the body at point A.Total energy of the body at point D = [ kinetic energy + potential energy] at point D.Applying the law of conservation of energy at point A and D, we haveTotal energy of the body at point A = Total energy of the body at point D⇒mgh1=12mu2+mgh12⇒h1=12u2g+h12⇒1=12u210+12⇒u2=12×20⇒u=10m/sThe body falls from point D at a height of 0.5 m, towards the ground with velocity u, following a parabolic trajectory.Since the body is projected horizontally at point D, its initial velocity component along the downward direction, i.e. uy is zero.u=10 m/sat point D horizantal componant of u=0v2=u2+2g sSoV2=(0)2+2×10×s(10)2=2×10×ss=102×10=12s=12Hence, the correct option is (A).