Physics 12 Assignment KEY 2-D Collisions & Projectile Motion

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1 Physics 1 ssignment KEY -D Collisions & Projectile Motion -D Collisions: 1. Define the following terms: Elastic collision - a collision in which both momentum and kinetic energy are consered Inelastic collision - a collision in which only momentum is consered Law of Conseration of Momentum the total momentum of all objects before a collision equal the total momentum of all objects after the collision Oblique (or glancing) collision a collision in two dimensions. What are the conditions for an oblique collision to be erfectly elastic? Collision must be oblique The two objects hae identical masses One of the masses is initially stationary The searation angle is a right angle 3. 5 kg object moing at 3. m/s east collides and sticks to an 18 kg object moing at 4.1 m/s north. What is the seed in m/s of the combined mass just after the collision? Include an aroriately scaled momentum ector diagram in your resonse. 4. radioactie nucleus at rest decays into a second nucleus, an electron and neutrino. The electron and neutrino are emitted at right angles and hae momenta of 9.3 x 10-3 kg m/s and 5.4 x 10-3 kg m/s resectiely. What is the magnitude and direction of the recoiling nucleus? Include a roer momentum ector addition diagram in your answer. ecause the initial momentum is zero, the momenta of the three roducts of the decay must add to zero. If we draw the ector diagram (see right), we see that: We find the angle from:

2 5. billiard ball of mass m kg moing with a seed 1.80 m/s strikes a second ball, initially at rest, mass of m kg. s a result of the collision, the first ball is deflected off at an angle of 30.0 o with a seed of 1.10 m/s. (a) Taking the x-axis to be the original direction of motion of ball a, write down the equations exressing the conseration of momentum for the comonents in the x and y directions searately. (b) Sole these equations for the seed,, and angle, θ, of ball. Do not assume the collision is elastic. Include a roer momentum ector addition diagram in your answer. 6. Car with a mass of 1.70 x 10 3 kg is traeling directly northeast at a seed of 14.0 m/s, and collides with car with a mass of 1.30 x 10 3 kg that is traeling directly south at a seed of 18.0 m/s. The two cars stick together during the collision. With what eloci does the tangled mass of metal moe immediately after the collision? Include a roer momentum ector addition diagram in your answer. Vector addition diagram: x y 45 o t θ

3 m (1700kg )(14.0m ) 3800kgm m (1300kg )(18.0 m ) 3400kgm o y x 3800 sin kgm y + y kgm x + x kgm t t ( 6600kgm ) 18000kgm + (16800kgm ) tanθ 6600 θ 69 m 18000kgm (3000kg) 6.0m 6.0m/s, [S69 o E] Projectile Motion: 7. Define the following terms: Trajectory - the ath described by an object moing due to a force or forces Projectile - an object that is gien an initial thrust and allowed to moe through sace under the force of grai only Range - the horizontal distance a rojectile traels 8. ball is thrown horizontally from the roof of a building 56 m tall and lands 45 m from the base. What was the ball s initial seed? We choose a coordinate system with the origin at the release oint, with x horizontal and y ertical, with the ositie direction down. We find the time of fall from the ertical dislacement:

4 1 1 The horizontal motion will hae constant eloci. We find the initial seed from kg ball is kicked on a leel field with a seed of 1 m/s at an angle of 63 aboe the ground. How long, in seconds, will the ball be in the air during its flight? Since the ball is kicked from ground leel and lands at ground leel, one can use the symmetry of its arabolic trajectory. The initial ertical eloci is: yi (1 m/s)(sin 63 o ) m/s t the to of its trajectory, then: yf 0 m/s Thus, t ( yf iy )/g (0 m/s m/s)/(-9.81 m/s ) t s. Due to symmetry, t s x.18 s 10. rojectile is shot from the edge of a cliff 15 m aboe the ground leel with an initial seed of 105 m/s at an angle of 37.0 o with the horizontal, as shown in the figure below. (a) Determine the time taken by the rojectile to hit oint P at ground leel. (b) Determine the range X of the rojectile as measured from the base of the cliff. t the instant just before the rojectile hits oint P, find (c) the horizontal and the ertical comonents of its eloci, (d) The magnitude of the eloci, and (e) the angle made by the eloci ector with the horizontal. (a) We choose a coordinate system with the origin at the base of the cliff, with x horizontal and y ertical, with the ositie direction u. We find the time required for the fall from the ertical motion:

5 which gies t 1.74, 14.6 s. ecause the rojectile starts at t 0, we hae t 14.6 s. (b) We find the range from the horizontal motion: (c) For the eloci comonents, we hae (d) When w e combine these comonents, we get (e) We find the angle from