A child in a boat throws a 5.90-kg package out horizontally with a speed of 10.0 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 28.0 kg and that of the boat is 35.0 kg . (Take the package's direction of motion as positive.)

0.94 m/s opposite the direction of the package

Explanation:

From the law of conservation of momentum,

Total momentum before the throw = Total momentum after the throw.

Note: Assuming the child, the boat and the package, where initially at the same velocity

U(m+m'+m'') = V(m+m')+v''(m'') Equation 1

Note: since the boat was initially at rest, U = 0 m/s

0 = V(m+m') + v'(m'')

-V(m+m') = v''(m'') Equation 2

Where,

V = Velocity of the boat immediately after the throw, m = mass of the child, m' = mass of the boat, m'' = mass of the package, v'' = velocity of the package after the throw.

make V the subject of the equation

V = -v''(m'')/(m+m') Equation 3

Given: v'' = 10 m/s, m'' = 5.9 kg, m = 28 kg, m' = 35 kg

Substitute into equation 3

V = -10(5.9)/(28+35)

V = -59/63

V = -0.94 m/s.

The Negative sign shows that the velocity of the both immediately after the throw is in opposite direction to the velocity of the package

a and b sometimes have a positive value

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force