Question

An object at rest explodes into three pieces. Two, each of the same mass, fly off in different directions with velocity 50 m/s and 100 m/s, respectively. A third piece is also formed in the explosion, and has twice the mass of the first two pieces. What is the magnitude and direction of its velocity?

Answer 1

Answer:

$v = 55.9 m/s$

direction is given as

$\theta = 63.4 degree$

Explanation:

As per momentum conservation we can say that since there is no external force on the system

so here total momentum must remains same

so here we will have

$m_1v_1 + m_2 v_2 + m_3 v_3 = 0$

so we have

$m(50 \hat i) + m(100 \hat j) + (2m) v_3 = 0$

so we will have

$v_3 = -(25 \hat i + 50 \hat j)$

so magnitude of the speed is given as

$v = \sqrt{25^2 + 50^2}$

$v = 55.9 m/s$

direction is given as

$\theta = tan^{-1}\frac{50}{25}$

$\theta = 63.4 degree$