Question

An explosion blows a rock into three parts. two pieces go off a right angle to each other 1.0 kg pieces with the velocity 12m/s
and other 2.0kg pieces with v=8m/s . If the third flies of with a v=40m/s. Compute the mass of third piece ​

Answer 1

Answer:

Let m

1

,m

2

and m

3

be the masses of the three pieces. m

1

=1.0kg,m

2

=2.0kg

Let ν

1

=12m/s,ν

2

=8m/s,ν

3

=40m/s. Let ν

2

be directed along x-axis, respectively and ν

3

be directed as shown.

By the principle of conservation of momentum, initial momentum is zero. Hence,

along x−axis:0=m

1

ν

1

−m

3

ν

3

Cosθ

along y−axis:0=m

2

ν

2

−m

3

ν

3

Cosθ

⟹m

1

ν

1

=m

3

ν

3

Cosθ and m

2

ν

2

=m

3

ν

3

Cosθ

By squaring and adding, we get m

1

2

ν

1

2

+m

2

2

ν

2

2

=m

3

2

ν

3

2

m

2

3

=

(40)

2

1

2

(12)

2

+(2)

2

(8)

2

⟹m+3=0.5kg