**Problem 3:**A 95.5-kg football player running north at 6.25 m/s is tackled by a 105-kg player running south at 4.90 m/s. If they stick together during the collision, what is the magnitude and direction of their velocity right after the collision?**Explanation:**This problem involves an inelastic collision where two objects stick together after colliding. We can solve this using the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.- **Step 1:** Calculate the momentum of each player before the collision. - Momentum is mass times velocity. - For the north-running player: \( p_1 = 95.5 \, \text{kg} \times 6.25 \, \text{m/s} \) - For the south-running player: \( p_2 = 105 \, \text{kg} \times (-4.90) \, \text{m/s} \) (Note: The south direction is considered negative.)- **Step 2:** Add the momenta to find the total momentum before the collision. - **Step 3:** Use the conservation of momentum to find the velocity of the combined mass after the collision. - Total mass = \( 95.5 \, \text{kg} + 105 \, \text{kg} \) - Solve for velocity using: \[ v_{\text{final}} = \frac{p_{\text{total}}}{\text{total mass}} \]- **Result:** This velocity will provide both the magnitude and direction because the sign will indicate the direction (positive for north, negative for south).

Given data: Mass of first player (m1) = 95.5 kg Initial velocity of first player (V1) = +6.25 m/s Mass of second player (m2) = 105 kg Initial velocity of second player (V2) = -4.90 m/s After collision players stick together Required: The magnitude and direction of the two players velocity after the collision According to conservation of momentum The total momentum of the system is remains constant. Total initial momentum = Total final momentum m1v1+m2v2=(m1+m2)vfvf=m1v1+m2v2m1+m2= 95.5kg(+6.25m/s) + (105kg)(-4.90m/s)95.5kg + 105 kg=+0.4108 m/s≈ +0.411 m/s Here, positive sign shows that the direction of the final velocity is towards North The magnitude of the two players velocity after the collision is 0.411 m/s Direction: North Answer: 0.411 m/s, North

Science

Physics

A 95.5-kg football player running north at 6.25 m/s is tackled by a 105-kg player running south at 4.90 m/s. If they stick together during the collision, what is the magnitude and direction of their velocity right after the collision?

A 95.5-kg football player running north at 6.25 m/s is tackled by a 105-kg player running south at 4.90 m/s. If they stick together during the collision, what is the magnitude and direction of their velocity right after the collision?

College Physics

11th Edition

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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