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Collision in Two-Dimensions #8211; Oblique collision The collision after which the direction of velocity of bodies make some angle with the direction of velocities of body before the collision is known as oblique collision. Consider two objects, P of mass m<sub>1</sub>. Moving with speed u along X #8211; axis and Q of mass m<sub>2</sub> at rest. Suppose, the collision is oblique (not head #8211; on) and m<sub>1</sub> moves with velocity v<sub>1</sub> at angle θ and m<sub>2</sub> with velocity v<sub>2</sub> at any angle ɸ as shown below. In this type of collision, we resolve the velocities in two mutually perpendicular axes. From conservation of linear momentum, (p<sub>x</sub>)<sub>i</sub> = (p<sub>x</sub>)<sub>f</sub> ⇒ m<sub>1</sub>u = (m<sub>1</sub> + m<sub>2</sub>)v<sub>x</sub> = m<sub>1</sub>v<sub>1</sub>cosθ + m<sub>2</sub>v<sub>2</sub> cos ɸ (p<sub>y</sub>)<sub>i</sub> = (p<sub>y</sub>)<sub>f</sub> ⇒ 0 = m<sub>1</sub>v<sub>1</sub>sinθ #8211; m<sub>2</sub>v<sub>2</sub>sin ɸ ⇒ v<sub>1</sub>sinθ = v<sub>2</sub>sin ɸ
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