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Problems on collision and Kepler's laws of planetary motion

1) In a certain road accident, a car of mass 1500 kg, traveling south, collided in the middle of an intersection with a truck of mass 7500 kg, traveling west. The vehicles locked and skidded off the road along a line pointing almost exactly southwest. A witness claimed that the truck had entered the intersection at 55 mph. Do you believe the witness? To decide, calculate the speed at which the car must have entered the intersection for this situation to occur. Enter the speed of the car.

2) The sun appears to be moving at a speed of about 240 km/s in a circular orbit of radius about 27000 light-years around the center of our galaxy. The earth takes 1 year to describe an almost circular orbit of radius about 1.5×10^11 m around the sun. What do these facts imply about the total mass responsible for keeping the sun in its orbit? Obtain this mass as a multiple of the sun's mass M.

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Solution:

Problem 1

Car (Mass = 1500 kg)

V

X
55 mph 45O
Y
Truck (Mass = 7500 kg) V'

Let the initial speed of car be V mph and after collision speed of (truck+car) be V' mph. This is a case of perfectly inelastic collision. We shall apply conservation of momentum (which applies to any collision, elastic or inelastic) along X axis and Y axis.

Net momentum after collision along X axis = Net momentum before collision along X axis

Total mass of truck & car x X component of speed V' = Mass of truck x Initial speed of truck [car has ...

Solution Summary

The solution assists with providing the detailed step-by-step answers to the problems on collision on Kepler's Laws of Planetary Motion.

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