Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

A 7.00 kg ball hits a 75.0 kg man standing at rest on ice. The man catches the ball. How fast does the ball need to be moving in order to send the man off at a speed of 3.00 m/s?

Sagot :

Supernova

Answer:

35.14 m/s

Explanation:

The Law of Conservation of Momentum states that the momentum before and after a collision is the same.

  • m₁ v₁ + m₂ v₂ = m₁ v₁ + m₂ v₂

Let's set the ball to have the subscript of 1 and the man to have the subscript of 2.

The initial and final mass of the ball is the same, so m₁ = 7.00 kg on both sides of the equation.

The initial velocity of the ball, v₁ on the left side of the equation, is the unknown variable we are trying to find.

The initial and final mass of the man is the same, so m₂ = 75.0 kg on both sides of the equation.

The man starts at rest, meaning that his initial velocity is v₂ = 0 m/s on the left side of the equation.

The final velocity of both the ball and the man is 3.00 m/s, so we can set v₁ and v₂ on the right side of the equation to equal 3.00 m/s.

Left side of the equation:

  • m₁ = 7.00 kg
  • v₁ = ?
  • m₂ = 75.0  kg
  • v₂ = 0 m/s

Right side of the equation:

  • m₁ = 7.00 kg
  • v₁ = 3.00 m/s
  • m₂ = 75.0  kg
  • v₂ = 3.00 m/s  

Substitute these values into the Law of Conversation of Momentum formula.

  • (7.00) v₁ + (75.0)(0) = (7.00)(3.00) + (75.0)(3.00)

Multiply and simplify.

  • 7.00 v₁ = 21 + 225
  • 7 v₁ = 246

Divide both sides of the equation by 7.

  • v₁ = 35.14 m/s

The ball needs to be moving at a speed of 35.14 m/s in order to send the man off at a speed of 3.00 m/s.

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.