**Problem Statement:**A 0.10 kg ball is launched with an initial velocity \( v_{i, \text{ball}} \) into a stationary cup with a mass of 0.15 kg. After the perfectly inelastic collision, the two objects travel together with a velocity of 0.605 m/s. Determine the initial velocity of the ball. (Hint: use the Conservation of Momentum Equation).**Diagram Explanation:**- **Ball:** The mass of the ball (\( m_{\text{ball}} \)) is given as 0.10 kg.- **Cup:** Depicted as a stationary object with mass 0.15 kg.- **Combined System Velocity:** After the collision, both objects move together at a velocity of 0.605 m/s. There is a graphical representation showing a cup and ball system suspended with a pivot point. The ball, initially moving horizontally, is represented with an arrow indicating its unknown initial velocity \( v_{i, \text{ball}} \). The resultant velocity of the ball and cup system is labeled as \( v_{i, \text{ball} + \text{cup}} = 0.605 \, \text{m/s} \). The masses are clearly labeled in the diagram, but there is a typographical error indicating \( m_{\text{ball}} = 10 \, \text{kg} \) instead of 0.10 kg.Use the conservation of momentum to find the initial velocity of the ball:\[m_{\text{ball}} \times v_{i, \text{ball}} = (m_{\text{ball}} + m_{\text{cup}}) \times v_{i, \text{ball+cup}}\]

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Description: **Problem Statement:**A 0.10 kg ball is launched with an initial velocity \( v_{i, \text{ball}} \) into a stationary cup with a mass of 0.15 kg. After the perfectly inelastic collision, the two objects travel together with a velocity of 0.605 m/s. D

Given, Mass of ball , mball = 0.10 kg Mass of cup , mcup = 0.15 kg After the perfectly inelastic collision , the two object travel with a velocity of 0.605 m/s. We have to calculate the initial velocity of ball , vi,ball and vi,cup = 0 m/s From conservation of momentum , mball×vi,ball+mcup×vi,cup = mball+mcup×0.605 m/sSo, 0.10kg×vi,ball+0.15kg×0m/s =(0.10kg+0.15kg)×0.605m/svi,ball =0.25kg×0.605m/s0.10kg =1.51 m/s Initial velocity of ball is 1.51 m/s.

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3. A 0.10 kg ball is launched with an initial velocity Vi,ball into a stationary cup with mass 0.15 kg. After the perfectly inelastic collision, the two objects travel with a velocity of 0.605 m/s. Determine the initial velocity of the ball. (Hint: use the Conservation of Momentum Equation). mball Vi ball 10 kg ball Pivot point ? V L m Vi,ball+cup=0.605. S

3. A 0.10 kg ball is launched with an initial velocity Vi,ball into a stationary cup with mass 0.15 kg. After the perfectly inelastic collision, the two objects travel with a velocity of 0.605 m/s. Determine the initial velocity of the ball. (Hint: use the Conservation of Momentum Equation). mball Vi ball 10 kg ball Pivot point ? V L m Vi,ball+cup=0.605. S

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Problem Statement:**

A 0.10 kg ball is launched with an initial velocity \( v_{i, \text{ball}} \) into a stationary cup with a mass of 0.15 kg. After the perfectly inelastic collision, the two objects travel together with a velocity of 0.605 m/s. Determine the initial velocity of the ball. (Hint: use the Conservation of Momentum Equation).

**Diagram Explanation:**

- **Ball:** The mass of the ball (\( m_{\text{ball}} \)) is given as 0.10 kg.
- **Cup:** Depicted as a stationary object with mass 0.15 kg.
- **Combined System Velocity:** After the collision, both objects move together at a velocity of 0.605 m/s.

There is a graphical representation showing a cup and ball system suspended with a pivot point. The ball, initially moving horizontally, is represented with an arrow indicating its unknown initial velocity \( v_{i, \text{ball}} \). The resultant velocity of the ball and cup system is labeled as \( v_{i, \text{ball} + \text{cup}} = 0.605 \, \text{m/s} \). The masses are clearly labeled in the diagram, but there is a typographical error indicating \( m_{\text{ball}} = 10 \, \text{kg} \) instead of 0.10 kg.

Use the conservation of momentum to find the initial velocity of the ball:

\[
m_{\text{ball}} \times v_{i, \text{ball}} = (m_{\text{ball}} + m_{\text{cup}}) \times v_{i, \text{ball+cup}}
\]

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