A ball falls from rest at a height H above a lake. Let y = 0 at the surface of t

Question

A ball falls from rest at a height H above a lake. Let y = 0 at the surface of the lake. As the ball falls, it experiences a gravitational force -mg. When it enters the water, it experiences a buoyant force B so the net force in the water is B - mg.

a) Write an expression for v(t) and y(t) while the ball is falling in air.

b) In the water, let v2(t) = at + b and y2(t) = (1/2)at2 + bt + c where a = (B - mg)/m. Use continuity conditions at the surface of the water to find the constants b and c.

I think for a) is

a) v(t) = -gt and y(t) = (-1/2)gt^2 + H.

Can someone help me with b) ? Thank you.

Explanation / Answer

v =gt

y = H-0.5gt^2

b) sqrt(2gh) = (B - mg)*sqrt(2h/g)/m +b

b = sqrt(2gh) - (B - mg)*sqrt(2h/g)/m

-c = (1/2)at2 + bt

c = -(0.5*B - mg)*(2h/g)/m)-sqrt(2h/g)*(sqrt(2gh) - (B - mg)*sqrt(2h/g)/m)

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