Three objects A, B, C are at vertices P, Q and R respectively of square PQRS of side 1km speed of these objects are 36km/hr 10m/s 0.8km/min initially they are at rest and start moving in clockwise direction simultaneously
1) By what time A reaches vertex Q distance between the objects B and C is -----kms
3/4. 4/3. 5/6. 6/5
2) Time after A will meet B is
1min20sec. 1min. 1min30sec. 1min40sec
3) Time after which all of them are at starting position is?
1min. 18min. 20min. 30min
To answer these questions, we need to calculate the distances between the objects at different time intervals.
Let's analyze the motion of each object and calculate the distances:
1) By what time A reaches vertex Q, the distance between objects B and C is:
- Object A travels from P to Q, which is one side of the square, so the distance is 1km.
- Object B travels from Q to R, which is another side of the square, so the distance is 1km.
- Object C travels from R to S, which is the third side of the square, so the distance is 1km.
Therefore, the distance between objects B and C remains constant at 1km.
2) To calculate the time when A meets B, we need to determine when they reach the same point.
- Object A takes 1km at a speed of 36km/hr. To convert km/hr to m/s, we use the conversion factor 1 km = 1000 m and 1 hr = 3600 sec:
Speed of A = 36km/hr = (36 * 1000m) / (3600 s) = 10 m/s.
- Object B travels from Q to R, which is a side of length 1km, with a speed of 10 m/s.
Time taken by B = Distance / Speed = 1km / 10m/s = 1000m / 10m/s = 100s = 1min 40sec.
So, A meets B after 1min 40sec.
3) To determine when all the objects are back at the starting position, we need to find the time it takes for each object to complete a full circle (square).
- Object A completes one full circle in the time it takes for it to travel around the square, which is the perimeter of the square divided by its speed:
Time taken by A = Perimeter / Speed = 4km / 36km/hr = 4000m / (36 * 1000m / 3600s) = 4000m / (10 m/s) = 400s = 6min 40sec.
- Object B also completes one full circle in the same time as A, as they have the same speed.
Time taken by B = 6min 40sec.
- Object C completes one full circle in the time it takes for it to travel around the square (perimeter) divided by its speed:
Time taken by C = Perimeter / Speed = 4km / 0.8 km/min = 4000m / (0.8 * 1000m / 60s) = 4000m / (0.8 m/s) = 5000s = 1hr 23min 20sec.
Therefore, all objects are back at the starting position after 6min 40sec.
To summarize:
1) The distance between objects B and C is 1km.
2) A meets B after 1min 40sec.
3) All objects are back at the starting position after 6min 40sec.