Tiêu đề Target Exam 05_English.pdf ✅

AL / 2025 / 10 / E - II (NEW) – TARGET EXAM 05 - 2 - Combined Mathematics Ruwan Darshana 1. Two particles A and B, each of mass λm and m respectively, simply collide while moving on a smooth horizontal ground in the same straight line to the same direction. The velocities of A and B just before the collision are λu and u respectively. The coefficient of restitution between A and B is 1 λ .(λ > 1). Show that the velocity of B just after the collision is λu. λ Find the impulse created between A and B during the collision in terms of λ, m , u. 2. A particle is projected from a point O on the top of a hill of height 3a with an initial velocity of √2ga and at an angle α (0 < α < π 2 ) with the horizontal. The particle hits the ground at a point 4a horizontal distance from O. Show that α = tan−1 ( 1 2 ). 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[See page three. √2ga
AL / 2025 / 10 / E - II (NEW) – TARGET EXAM 05 - 3 - Combined Mathematics Ruwan Darshana 3. One end of a light inextensible string is connected to particle P of mass m which is placed on a midpoint of smooth plane at an inclination of π 6 with horizontal. Other end of string passes below over the smooth pulley Q of mass λm and connected to the particle R of mass 2m which is placed on smooth horizontal plane. If the time taken for the particle P to reach top edge of the smooth inclined plane is 2 √ 7a g , Then find λ. (Total length of inclined plane is 6a). 4. A car of mass M is pulled by a string along a horizontal ground by a car of mass 2M. When the velocity of the system is v and the acceleration is a 2 , the engine power of the car of mass 2M is 2H 3 . When the velocity of the system is v and the acceleration is a, the engine power of the car of mass 2M is H.If the external resistance force on the system is constant in both cases, find that external resistance force. Show that a = 2H 9Mv . .............................................................................................................................................................................................. .............................................................................................................................................................................................. .............................................................................................................................................................................................. .............................................................................................................................................................................................. .............................................................................................................................................................................................. 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[See page four. π 6 ⁄