Question

Question #e0d7b

Answer 1

The recoil of the Earth will be equal to `-1.7 * 10^(-24)"m/s"`.

Explanation:

So, you know that a 5-kg bowling ball is projected upward with a velocity of 2 m/s.

Consider your bowling ball - Earth system. Before launching the bowling ball, the net momentum of this system is zero. After the ball is launched, it develops a positive momentum given by its upward speed and mass.

`p_"bowling" = m_"bowling" * v_"initial"`

However, the net momentum of the bowling ball - Earth system must be preserved, which means that the Earth will also develop a momentum.

If you take the upward direction to be the positive one, then the velocity of the Earth will carry a negative sign, since it's pointed in the opposite direction. So,

`0 = p_"bowling" + p_"Earth"`

`0 = m_"bowling" * v_"initial" + m_"Earth" * v_"Earth"`

Regroup this equation to get the recoil velocity of the Earth

`v_"Earth" = - m_"bowling"/m_"Earth" * v_"initial"`

`v_"Earth" = - (5cancel("kg"))/(6 * 10^(24)cancel("kg")) * "2 m/s"`

`v_"Earth" = color(green)(-1.7 * 10^(-24)"m/s")`

The negative sign just symbolizes that the direction of movement is opposite to that of the bowling ball.