KVPY SB SX Exam 2011 Question Paper

Question : 100 of 120

Marks: +1, -0

A particle moves in a plane along an elliptic path given by

x^2/a^2+y^2/b^2=1.

At point (0, b), the x-component of velocity is u. The y-component of acceleration at this point is

Solution:

x^2/a^2+y^2/b^2=1

u_x = u

at (0, b)

u_y = 0

{2x}/a^2{dx}/{dt}+{2y}/b^2{dy}/{dt}=0

Again diff. w.r.t. to time

{2x}/a^2{d^2x}/{dt^2}+2/a^2({dx}/{dt})^2

+{2y}/b^2{d^2y}/{dt^2}+2/b^2({dy}/{dt})=0

acceleration at (0, b) is

a_y=-b/a^2u^2

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