A 2.0-kilogram cart that is moving due east at 6.0 meters per second collides with a 4.0-kilogram cart moving due west. The carts stick together and move due west at 1.0 meters per second after the collision. What is the initial speed of the of 4.0-kilogram cart before the collision?

The initial velocity of the 4-kg cart before the collision is -1.5 m/s.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

A collision is an event in which two or more objects exert forces on each other for a short duration of time. It can be either inelastic or elastic collision. A completely inelastic collision is a special case where the two objects stick together and move with a common final velocity after the collision. Here, it is given that the carts stick together after the collision. This implies that it is an inelastic collision.

The inelastic collision formula is given by

`m_1v_1+m_2v_2=(m_1+m_2)v_f`

where

`m_1` is the mass of object 1

`m_2` is the mass of object 2

`v_1` is the velocity of object 1

`v_2` is the velocity of object 2

`v_f` is the final velocity of the two objects.

From the question, we have,

`m_1=2\ kg` , `v_1=6 ` m/s moving due east

`m_2 = 4\ kg`

`V=1` m/s

Here, we have to find out the initial velocity `v_2` of the cart having mass 4kg moving due west.

Substituting the known values in the above formula, we get,

`2 \times 6+4\times v_2=(2+4)\times 1 `

i.e. `12+4v_2=6`

`4v_2=-6`

`v_2=\frac{-6}{4} = -1.5` m/s

Therefore, the initial velocity of the 4kg cart before the collision is -1.5 m/s.

Last Updated by eNotes Editorial on
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial