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3 years ago

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A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of ma

ss m, moves with velocity (-47 m/s) and a second piece, also of mass m, moves with velocity (-47 m/s) . The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the +x axis) of the velocity of the third piece?

1 answer:

Sholpan [36]3 years ago

4 0

Answer:

a) 22.06m/s

b)45°

Explanation:

Let 'm' be mass of 1st and 2nd pieces

mass of 3rd piece=3m

$v_{1}$ =velocity of 1st piece = -47iˆ m/s

$v_{2}$ =velocity of 2nd piece = -47jˆ m/s

$v_{3}$ =velocity of 3rd piece=?

By considering conservation of linear momentum, we have

m $v_{1}$ + m $v_{2}$ + 3m $v_{3}$ =0

$v_{1}$ + $v_{2}$ + 3 $v_{3}$ =0

3 $v_{3}$ = - ( $v_{1}$ + $v_{2}$ )

$v_{3}$ = - $\frac{1}{3}$ ( $v_{1}$ + $v_{2}$ )

Substituting the values of $v_{1}$ and $v_{2}$ in above equation

$v_{3}$ = - $\frac{1}{3}$ (-47iˆ -47jˆ ) => 15.6iˆ + 15.6jˆ

(a)Magnitude of the velocity of the third piece is given by

| $v_{3}$ | =√15.6²+15.6² => 22.06m/s

(b) its direction (as an angle relative to the +x axis) 'θ'

θ= $tan^{-1} (\frac{15.6}{15.6} )$ => $tan^{-1} (1 )$ =>45°

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