girl of mass 40kg having v 2m/s jumps on a stationary cart of mass 4 kg find the velocity of girl when the cart starts moving

M1*V1 + M2*V2 = M1*V + M2*V

40*2 + 4*0 = 40V + 4V
44V = 80
V = 1.82 m/s.

To find the velocity of the girl after the cart starts moving, we can use the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.

Let's assume the velocity of the girl after the cart starts moving is v_g (final velocity of the girl) and the velocity of the cart after the girl jumps on it is v_c (final velocity of the cart). The mass of the girl is 40 kg, and the mass of the cart is 4 kg.

Before the interaction, the girl jumps with a velocity of 2 m/s, and the cart is stationary, so the initial momentum is:
Girl's momentum = mass of the girl × velocity of the girl = 40 kg × 2 m/s = 80 kg·m/s

The cart is initially stationary, so its initial momentum is:
Cart's momentum = mass of the cart × velocity of the cart = 4 kg × 0 m/s = 0 kg·m/s

After the interaction, the total momentum is conserved, so:
Total momentum before = Total momentum after
80 kg·m/s + 0 kg·m/s = (40 kg + 4 kg) × (v_g + v_c)

Simplifying the equation:
80 kg·m/s = 44 kg × (v_g + v_c)

Now, we can divide both sides of the equation by 44 kg to solve for the final velocity of the girl (v_g):
80 kg·m/s / 44 kg = v_g + v_c

Simplifying further:
1.82 m/s = v_g + v_c

Since the cart was initially stationary, the final velocity of the cart (v_c) will be equal in magnitude but opposite in direction to the final velocity of the girl (v_g). So, we can rewrite the equation as:
1.82 m/s = v_g + (-v_g)

Simplifying this equation:
1.82 m/s = 0 m/s

Therefore, the final velocity of the girl (v_g) when the cart starts moving is 0 m/s.