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)which of the objects have the maximum speed?
A. B. C. SAME SPED?
2)By what time A reaches vertex Q distance between the objects B and C is -----kms
3/4. 4/3. 5/6. 6/5
3)Time after A will meet B is
1min20sec. 1min. 1min30sec. 1min40sec
4) Time after which all of them are at starting position is?
1min. 18min. 20min. 30min
For comparison, change all to m/s:
36 km/hr = 36000m/3600s = 10 m/s
.8km/min = 800m/60s = 13.33 m/s
A takes 100 seconds to reach Q.
By that time,
B has reached R
C has passed S and is 33.33 m toward P
So, BC = √(1000^2 + 33.33^2) meters
Since A and B are both moving at 10 m/s, A will never catch B.
C is moving 4/3 as fast as A and B. It will travel 4 times around PQRS while they go 3 laps. So, all will be back home after 300 seconds.
Check my math and check for typos, since #3 has no solution.
To answer the given questions, we need to determine the speeds and positions of objects A, B, and C.
Let's start by calculating the speeds of objects A, B, and C in terms of km/hr:
- Object A: 36 km/hr
- Object B: 10 m/s = 10 * (18/5) km/hr ≈ 36 km/hr
- Object C: 0.8 km/min = 0.8 * 60 km/hr = 48 km/hr
1) To determine which object has the maximum speed, we can compare their speeds:
- Object A: 36 km/hr
- Object B: 36 km/hr
- Object C: 48 km/hr
Therefore, object C has the maximum speed.
2) To determine the time it takes for object A to reach vertex Q while the distance between objects B and C is certain, we need to consider the direction of their movement. Since they are moving in a clockwise direction, object A moves from vertex P to Q, passing both objects B and C.
The distance between P and Q along the square's side is 1 km.
Therefore, the distance between objects B and C when A reaches vertex Q is 1 km.
3) To determine the time when objects A and B will meet, we need to consider the distances they need to cover while moving in a clockwise direction.
- Object A: 36 km/hr
- Object B: 36 km/hr
Since they have the same speed, they will meet after covering the same distance. Since the square has a perimeter of 4 km, they will meet after 1 hour of moving.
Therefore, they will meet after 1 hour (or 60 minutes).
Converting the time to minutes and seconds:
1 hour = 60 minutes
1 minute = 60 seconds
4) To determine the time when all three objects will be back at the starting position, we need to consider the time it takes for object C to complete one full rotation around the square.
- Object C: 48 km/hr
To calculate the time it takes for object C to complete one full rotation, we divide the perimeter of the square by the speed of object C:
4 km / 48 km/hr = 4/48 hr = 1/12 hr = 5 minutes
Therefore, all three objects will be back at the starting position after 5 minutes.
Converting the time to minutes:
5 minutes
So, the answers to the questions are:
1) Object C has the maximum speed.
2) The distance between objects B and C when object A reaches vertex Q is 1 km.
3) Objects A and B will meet after 1 hour (or 60 minutes).
4) All three objects will be back at the starting position after 5 minutes.