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A 20gball of clay traveling east at 3.0m/s collides with a 30g ball of clay traveling north at 2.0m/s. What are the speed and the direction of the resulting 50g ball of clay? Give your answer as an angle north of east.

Short Answer

Expert verified

The speed of the 50gball is 1.7m/s, angle is450north of east

Step by step solution

01

Step 1. Given information

Mass of clay ball 1,mClayball1=20g

Mass of clay ball 2,mclayball2=30g

The velocity of clay ball 1,v1=3m/s

The velocity of clay ball 2,v2=2m/s

To evaluate speed of clay ball 3.

02

Step 2. Analyze

Clay 1 travels east (in positive x-direction), while clay 2 travels north (in a negative x direction) (positive y direction) clay no. 2 The velocity of the ensuing ball of clay (which we'll call clay 3), is represented as

v3=v3cosi+v3sinj

03

Step 3. Evaluating x-component

As we all know, each element's momentum is conserved individually.

For x-component,

p1x+p2x=p3x0.02kg3m/s+0=0.05kgv3cos

0.02kg3m/s+0=0.05kgv3cosv3cos=1.2m/s

04

Step 4. Evaluating y-component and final calculation for the 

For y-component,

p1y+p2y=p3y0+0.03kg.2m/s=0.05kgv3sinv3sin=1.2m/s

From both the components,

tan=1=45o

Now evaluating the velocity,

v322=1.2v3=1.7m/s

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