Two objects, A and B, collide. A has mass 2.0 kg, and B has mass 3.0 kg. The velocities before

Name: Problem 25, Chapter 6: Physics
Uploaded: 2021-08-14T10:41:03-08:00
Duration: 3 min 45 s
Channel: Mayank Tripathi
Description: Two objects, A and B, collide. A has mass 2.0 kg, and B has mass 3.0 kg. The velocities before the collision are 𝐯iA= (15 m / s) 𝐢̂+(30 m / s) 𝐣̂ and 𝐯i B=(-10 m / s) 𝐢̂+(5.0 m / s) 𝐣̂ After the collision, 𝐯fA=(-6.0 m / s) 𝐢̂+(30 m / s) 𝐣̂. What is the final velocity of B ?

step 1 So in this question, it is given to us that there are two bodies, A and B, which undergo collisi

Question

Two objects, $A$ and $B$, collide. A has mass $2.0 \mathrm{~kg}$, and $B$ has mass $3.0 \mathrm{~kg}$. The velocities before the collision are $\overrightarrow{\mathbf{v}}_{\mathrm{iA}}=$ $(15 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(30 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{v}}_{\mathrm{i} B}=(-10 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(5.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ After the collision, $\overrightarrow{\mathbf{v}}_{\mathrm{fA}}=(-6.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(30 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$. What is the final velocity of $B$ ?

   Two objects, $A$ and $B$, collide. A has mass $2.0 \mathrm{~kg}$, and $B$ has mass $3.0 \mathrm{~kg}$. The velocities before the collision are $\overrightarrow{\mathbf{v}}_{\mathrm{iA}}=$ $(15 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(30 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{v}}_{\mathrm{i} B}=(-10 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(5.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$
After the collision, $\overrightarrow{\mathbf{v}}_{\mathrm{fA}}=(-6.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(30 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$. What is
the final velocity of $B$ ?

Physics

Robert Resnick,… 5th Edition

Chapter 6, Problem 25

Instant Answer

Solved by Expert Mayank Tripathi

08/14/2021

Step 1

The mass of A is $2.0 \, \mathrm{kg}$ and the mass of B is $3.0 \, \mathrm{kg}$. The initial velocities of A and B are $\overrightarrow{\mathbf{v}}_{\mathrm{iA}}=(15 \, \mathrm{m/s}) \hat{\mathbf{i}}+(30 \, \mathrm{m/s}) \hat{\mathbf{j}}$ and Show more…

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Two objects, $A$ and $B$, collide. A has mass $2.0 \mathrm{~kg}$, and $B$ has mass $3.0 \mathrm{~kg}$. The velocities before the collision are $\overrightarrow{\mathbf{v}}_{\mathrm{iA}}=$ $(15 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(30 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{v}}_{\mathrm{i} B}=(-10 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(5.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ After the collision, $\overrightarrow{\mathbf{v}}_{\mathrm{fA}}=(-6.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(30 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$. What is the final velocity of $B$ ?

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Key Concepts

Conservation of Momentum

In a collision involving two or more objects, the total momentum of the system is conserved if no external forces act on it. This principle allows the use of the initial momentum values of all objects to determine unknown final momentum values after the collision by setting the sum of the initial momenta equal to the sum of the final momenta.

Vector Decomposition in Two Dimensions

In problems involving two-dimensional collisions, momentum is a vector quantity, meaning it has both magnitude and direction. To analyze such problems, the momentum vectors are broken down into their orthogonal components (typically x and y). Each component is treated separately in the conservation equations, allowing the simultaneous solution of equations to find unknown quantities in the given directions.

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