Question

Two particles of masses m₁and m₂ in projectile motion have velocities $\overrightarrow{v}$₁, and $\overrightarrow{v}$₂respectively at time t = 0. They strike at time t₀and their velocities become $\overrightarrow{v}$'₁ and $\overrightarrow{v}$'₂at time 2t₀while still moving in air. The value of

$\left| \left( m_{1}\overrightarrow{v}'_{1} + m_{2}\overrightarrow{v}'_{2} \right) - \left( m_{1}{\overrightarrow{v}}_{1} + m_{2}{\overrightarrow{v}}_{2} \right) \right|$ is

• A. Zero
• B. (m₁+m₂)gt₀
• C. 2(m₁ + m₂)g t₀
• D. $\frac{1}{2}$ (m₁ + m₂)g t₀

Answer 1

Answer: (C)

2(m₁ + m₂)g t₀

Answer 2

$\left| \left( m_{1}\overrightarrow{v}'_{1} + m_{2}\overrightarrow{v}'_{2} \right) - \left( m_{1}{\overrightarrow{v}}_{1} + m_{2}{\overrightarrow{v}}_{2} \right) \right|$

= change in momentum

= $\int_{}^{}{Fdt = 2\left( m_{1} + m_{2} \right)gt_{0}}$