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Chapter 11: Q. 47 (page 289)

A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at speed vo. The third piece has twice the mass as the other two. What are the speed and direction of the third piece? Give the direction as an angle east of north

Short Answer

Expert verified

The speed of the third piece is vo2at45o

Step by step solution

01

Step 1. Given information

A firecracker in a coconut blows the coconut into three pieces.

To find the speed of the third piece.

02

Step 2. Analyze and apply

We can conserve the momentum on both axis,

For x-axis:

m1v1,x+m2v2,x+m3v3,x=0m(-vo)+0+2mv3,x=0v3,x=v02

03

Step 3. Evaluating at y-axis

For y-component:

m1v1,y+m2v2,y+m3v3,y=0m(0)+m(-vo)+2mv3,y=0v3,y=vo2

The final speed, v=vx2+vy2=v02

The direction will be,tanθ=v3,yv3,x=1θ=45o

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