A 12000N automobile travels at a speed of40 km/h northward along a street, and a

Question

A 12000N automobile travels at a speed of40 km/h northward along a street, and a 8500 N sports cartravels at a speed of 62 km/h eastward along an intersectingstreet. a. If neither driver brakes and thecars collide at the intersection and lock bumpers, what will themagnitude of the velocity of the cars be immediately after thecollision? b. What will the direction of the velocity of the carsbe immediately after the collision? c. What percentage of the initialkinetic energy will be lost in the collision? A 12000N automobile travels at a speed of40 km/h northward along a street, and a 8500 N sports cartravels at a speed of 62 km/h eastward along an intersectingstreet. a. If neither driver brakes and thecars collide at the intersection and lock bumpers, what will themagnitude of the velocity of the cars be immediately after thecollision? b. What will the direction of the velocity of the carsbe immediately after the collision? c. What percentage of the initialkinetic energy will be lost in the collision? a. If neither driver brakes and thecars collide at the intersection and lock bumpers, what will themagnitude of the velocity of the cars be immediately after thecollision? a. If neither driver brakes and thecars collide at the intersection and lock bumpers, what will themagnitude of the velocity of the cars be immediately after thecollision? b. What will the direction of the velocity of the carsbe immediately after the collision? c. What percentage of the initialkinetic energy will be lost in the collision? c. What percentage of the initialkinetic energy will be lost in the collision?

Explanation / Answer

weight of auto mobile W = 12000 N mass of auto mobile M = W / g = 1224.48 kg weight of car w = 8500 N mass of car m = w / g = 867.34 kg Speed of auto mobile before collision  U = 40km / h                                                             = 40 * 5/ 18 m / s                                                             = 11.1111 m / s speed of car before collision  u = 62 km /h = 62 *5/ 18 m / s                                                = 17.222 m / s Let the velocity of the automobile and car after collisionbe  V and it makes an angle   with respect to east in east direction : ---------------------- from law of conservation of momentum , mu + 0 = ( m+ M) V cos                                               14937.52 = 2091.82 * V cos                                                      V cos = 7.14   ----( 1) In north direction : ------------------ from law of conservation of momentum , 0 + MU = ( m + M ) Vsin                                                                                                          13605.333 = 2091.82 * Vsin                                                     V sin = 6.5   ----( 2) eq ( 2) / eq ( 1 ) ==> tan = 0.9109                                         = 42.33 degrees from eq ( 1) velocity V = 7.14 / cos                                     = 9.658 m / s (a). the magnitude of the velocity of the cars be immediatelyafter the collision V = 9.658 m / s (b )the direction of the velocity of the cars beimmediately after the collision = 42.33 degrees                                                     V sin = 6.5   ----( 2) eq ( 2) / eq ( 1 ) ==> tan = 0.9109                                         = 42.33 degrees from eq ( 1) velocity V = 7.14 / cos                                     = 9.658 m / s (a). the magnitude of the velocity of the cars be immediatelyafter the collision V = 9.658 m / s (b )the direction of the velocity of the cars beimmediately after the collision = 42.33 degrees (b )the direction of the velocity of the cars beimmediately after the collision = 42.33 degrees                                                         

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