1. Prove that the maximum range of a projectile is attained at an angle of projection of 49". III. PROBLEM-SOLVING. Show all your complete solution to each problem to have partial credits. A. Impulse and Momentum 1. A school bus carrying 20 students has a mass of 2500 kg and moves with a speed of 4.25 m/'s. The driver has a mass of 70.0 kg. (a) What is the magnitude of the momentum of the bus and its passengers if the average mass of each student is 125 kg? (b) If eight students get off from the bus, what must be the speed of the bus to maintain its original momentum? 2. What is the momentum of the system of two particles with these respective masses and velocities: 3.75 kg moving north at 5.6 m/'s and 4.2 kg moving northwest at 2.3 m's? B. Impulse-Momentum Theorem Revised 1. A 500-kg body accelerates from 3.25 m's in 3.0 seconds when a force act upon it. Find (a) the change in momentum of the body, (b) the impulse produced by the force, and (c) the magnitude of the force. 2. A delivery truck hits a parked car from behind. the mass of the car is 2550 kg. What force is exerted on the car if (a) the car is rigid and accelerates to 4.5 m/'s in0.20 s? (b) the car has crumple zones and accelerates to 4.5 m's in 0.30s? C. Conservation of Linear Momentum 1. A 5.5 kg rifle fires an 11 g bullet with a velocity of 1000 m/'s. (a) what is the recoil velocity of the rifle? (b) If the shooter holds the rifle firmly against his shoulder, what will be the recoil velocity? Assume the mass of the shooter is 120 kg- D. Types of collision 1. Car A with a mass of 2000 kg moves at 72 ki/hr and B of mass 1250 kg travels at 60 km/hr. both approach each other and car A collides with car B. the cars then remain stuck together after collision. Find their velocity after the collision. determine if kinetic energy is lost. 2. A 6.5-kg bowling ball thrown with a speed of 5.4 m's hits a stationary 1.75-kg pin. What is the velocity of each object? Assume that the coefficient of restitution of 0.75. 3. The cue ball moving horizontally at 6.2 m's collided with a stationary billiard ball. As a result, the billiard ball is deflected 45" from the horizontal. find the speeds of the two balls and the angle the cue ball makes with the horizontal. Assume the collision is elastic and the masses of the balls are equal. 4. A car with a mass of 2500 kg and moving at 3m's northeast collided with a 3000 kg car moving northwest at 2.5 m/'s. find their final velocity.assume a perfectly inelastic collision
