A particle is moving with velocity ` vecv = k( y hat(i) + x hat(j)) `, where `k` is a constant . The genergal equation for its path is

Options

A. (a) `y^1 = x + constant
B. (b) ` xy = cosntant`
C. (c ) y^2 = x^2 + constatn
D. (d) ` y =x^2 + constant

Answer

C

Explanation

` vec v = K ( y hat I +x hat j) ` or ` v_x hat i+ v_y hat j = K (y hat i+ x hat j)`
:. ` v_x = Ky ` and ` v_y = K x`
` (dx) (dt) = Ky` or ` dx = Ky dt` ,brgt or ` x= Kyt` ….(i)
` (dy)/(dt) = Kx` or ` dy = Kx dt`
or ` y= Kxt` ….(ii)
From (i0, ` t= x/(Ky)`
From (ii), ` y = Kx (x/(Ky)) + a constant ltbRgt or ` y^2 = x^2 + a constant`.