A boat of mass 40 kg is at rest; A dog of mass 4 kg moves in the boat with a velocity of 10 m/s. what is the velocity of boat?

a) 4 m/s b) 2 m/s
c) 8 m/s d) 1 m/s

mv=(m+M)u

u=mv/(m+M) = 4•10/(4+40) = 0.9 m/s
d) 1 m/s

D) 1m/s

To solve this problem, we can apply the principle of conservation of momentum. The total momentum before the dog moves in the boat should be equal to the total momentum after the dog moves in the boat.

The momentum of an object is given by the product of its mass and velocity (momentum = mass * velocity).

Let's denote the velocity of the boat as Vb and the final velocity of the dog as Vd.

Before the dog moves in the boat, the boat is at rest, so the initial velocity of the boat (Vi) is 0 m/s.

Using the principle of conservation of momentum, we can write the equation:

Total momentum before = Total momentum after

(mass of boat * initial velocity of boat) + (mass of dog * initial velocity of dog)
= (mass of boat * final velocity of boat) + (mass of dog * final velocity of dog)

Substituting the given values:
(40 kg * 0 m/s) + (4 kg * 10 m/s)
= (40 kg * Vb) + (4 kg * Vd)

Simplifying the equation:
40 kg * 0 m/s + 4 kg * 10 m/s = 40 kg * Vb + 4 kg * Vd
0 kg*m/s + 40 kg*m/s = 40 kg * Vb + 4 kg * Vd
40 kg*m/s = 40 kg * Vb + 4 kg * Vd

Since the boat is at rest initially (Vi = 0 m/s), the equation further simplifies:
40 kg*m/s = 4 kg * Vd

Solving for Vd:
Vd = (40 kg*m/s) / (4 kg)
Vd = 10 m/s

So, the final velocity of the dog (or the velocity of the boat) is 10 m/s.

Therefore, the answer is not among the options given.