Question

Two masses, m and 2m, approach each along a path at right angles to each other. After collision, they stick together and move of at 2m/s at angle 37⁰ to the original direction of the mass m. What where the initial speeds of the two particles?

Answer 1

The initial speed of the object with mass "m" is 4.79 m/s and the initial speed of the object with mass "2m" is 1.81 m/s.

Initial speed of the two masses

The initial speed of the two masses is calculated by applying the principle of conservation of linear momentum as follows;

m₁u₁ + m₂u₂ = v(m₁ + m₂)

• let m be in horizontal direction
• let 2m be in vertical direction
• angle between the two masses = 90 degrees

in y - direction

$m_1u_1sin(\theta_1) + m_2u_2sin(\theta_2) = (m_1 + m_2)vsin(\theta_3)\\\\mu_1sin(0) + 2mu_2sin(90) = (m + 2m)(2)sin(37)\\\\2mu_2 = 3.61m\\\\u_2 = \frac{3.61 m}{2m} \\\\u_2 = 1.81 \ m/s$

in x - direction

$m_1u_1sin(\theta_1) + m_2u_2sin(\theta_2) = (m_1 + m_2)vsin(\theta_3)\\\\mu_1cos(0) + 2mu_2cos(90) = (m + 2m)(2)cos(37)\\\\mu_1 = 4.79 m\\\\u_1 = 4.79 \ m/s$

Thus, the initial speed of the object with mass "m" is 4.79 m/s and the initial speed of the object with mass "2m" is 1.81 m/s.

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