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Solved University-Physics Problems

Physics 1.-    Uniform Rectilinear Motion, URM

Javier Montenegro Joo

jmj@VirtualDynamics.Org

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[1] In the Amazonia two cities ‘A’ and ‘B’ are connected by a 300 km river going from ‘A’ to ‘B’.  A homemade boat traveling from ‘A’ to ‘B’ makes the journey in 12 hours and when returning, the journey takes 15 hours. Determine the speed of the river stream and the actual speed of the boat if there were no stream.

Solution.-

It is due to the direction of river stream, that the two journeys –covering the same distance- are made with different speeds. Obviously, when the river and the boat go in the same direction, the speed is higher than when river and boat go in opposite directions:

 

 

   

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[2] From two opposite sites 'A' and 'B' separated by a distance of 1250 km, two cars move off simultaneously, one to come across with the other, being their velocities respectively 90 km/hr and 120 km/hr. Determine the distances travelled by each car when they meet.

Solution.-

In the sketch below it can be seen that the sum of the distances travelled by ‘A’ and by ‘B’ equals the total separation between those points:

 
     
 

[3]  There are two towns ‘A’ and ‘B’ situated 180 km apart. A motorist going with a speed of 50 km/hr crosses ‘A’ when another motorist travelling at 35 km/hr   passes by ‘B’.  Both drivers travel in the direction from ‘A’ to ‘B’. Determine: (a) at what distance from ‘B’ both motorist meet (b) meeting time.

Solution.-

In the sketch below, assume that both drivers meet at point P at a distance x from point ‘B’ and at a distance 180 + x  from ‘A’.  The meeting time is the same for both pilots:

 
     
 

[4] Consider three cities, A, B and C, with C somewhere between A and B, which are 500 km apart.  There are two motorcyclists travelling in opposite directions, one of them going at 90 km/hr,  passes by A  when the other, going at 60 km/hr, passes by B. Determine how far from city C are the motorcyclists when they cross each other.

Solution.-

The sketch shows city C somewhere between A and B.  Point P is the crossing place. At crossing time motorcyclist A has travelled a distance XA  and B has covered XB  and, these two distances sum 500 km:

 
     
 

[5] Mary and Jane are at the same point on the sidewalk around a circular park of 196250 m², when they decide to start driving their bicycles along the sidewalk and, in opposite directions. While Mary displaces 100 m each minute, Jane covers 12 m each three seconds.  Determine the crossing time and the distances covered by both gals at the moment they meet.

Solution.-    

The sum of the distances covered by Mary and by Jane until they meet is equal to the length of the circumference.

 
     
     
     
     
     
     
 

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