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dear student,
solving on the pc is not possible you can buy arihant books to see the solutions or go to resonance website and place a order for rank master there you'll get the solutions.........its price is Rs.750, or check some old books from your seniors
It is a big question but the answer is rather easy
see rel vel of ball w.r.t trolley,
v(rel)=vcosψ i+ v sinψ j -(root{3}-1)j
say if some φ anghle is made by this vector
so tan φ = v sinψ - ( root3-1)/vcosψ. ........(1)
as the ball hits the trolley so the relative velocity is towards trolley; as a result the angle made by vel vector of ball w.r.t trolley is 45 with +ve X-axis
if ψ=4Θ/3, keep this value in(1). at t=0 & φ= 45 solve the equation and get the value of v which is 2m/s at 60 degree to X-axis
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