A boat of mass 250 kg is coasting, with its engine in neutral, through the water

Question

A boat of mass 250 kg is coasting, with its engine in neutral, through the water at speed 1.00 m/s when it starts to rain with incredible intensity. The rain is falling vertically, and it accumulates in the boat at the rate of 100 kg/hr art A What is the speed of the boat after time 0.500 hr has passed? Assume that the water resistance is negligible.Part C The drag is proportional to the square of the speed of the boat, in the form Fd=bv2 where b= 0.5 N s2/m2. What is the acceleration of the boat just after the rain starts? Take the positive x axis along the direction of motion..

Explanation / Answer

using conservation of momentum

Momentum initial = Momentum final

250 kg * 1m/s = (250 kg + (100 kg/hr * 0.5 hr))

300 V = 250

v=0.833m/sec

There will be change of the momentum which is equal to the forces acting on the boat. only the drag force, acts against the direction of motion. :

d(m·v)/dt = -Fd = - k·v²

a = dv/dt = - (k·v² + v·dm/dt) / m

= (0.5Ns²/m² · (1m/s)² + 1m/s · 100kg/3600s ) / 250kg

a=2.11*10^-3m/s^2

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