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A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car?
Most Upvoted Answer
A boy starts running with a constant velocity V towards a car which is...
Let the distance covered by Car be X in time t
so boy has to cover distance of 100+X in time t
so,
X=1/2at^2=t^2
Velocity of car after time t is Vc=at=2t(eq 1)
Velocity of man after time t is
Vm=S/t= (100+X)/t=(100+t^2)/t(eq 2)
The boy should have this minimum speed finally in order to catch the car
So,
Just equate the equation (1) and(2)
Vm=Vc
2t^2=100+t^2
t^2=100
t=10s
So,put value of t in eq(2)
V of man is 200/10=20m/s
so boy has to cover distance of 100+X in time t
so,
X=1/2at^2=t^2
Velocity of car after time t is Vc=at=2t(eq 1)
Velocity of man after time t is
Vm=S/t= (100+X)/t=(100+t^2)/t(eq 2)
The boy should have this minimum speed finally in order to catch the car
So,
Just equate the equation (1) and(2)
Vm=Vc
2t^2=100+t^2
t^2=100
t=10s
So,put value of t in eq(2)
V of man is 200/10=20m/s
Community Answer
A boy starts running with a constant velocity V towards a car which is...
**Solution:**
To find the value of V at which the boy will be able to catch the car, we need to determine the condition when the boy's distance from the starting point is equal to the car's distance from the starting point.
Let's analyze the motion of both the boy and the car separately.
**Motion of the Boy:**
- The boy starts running with a constant velocity V towards the car.
- The distance covered by the boy can be represented as:
`Distance covered by the boy = Velocity of the boy x Time taken by the boy`
- Let's assume the time taken by the boy to catch the car is t. Therefore, the distance covered by the boy can be written as:
`Distance covered by the boy = V x t`
**Motion of the Car:**
- The car starts from rest and has a constant acceleration of 2 m/sec^2 away from the man.
- The distance covered by the car can be represented using the equation of motion:
`Distance covered by the car = Initial velocity x Time + (1/2) x Acceleration x Time^2`
- Since the car starts from rest, the initial velocity of the car is 0.
`Distance covered by the car = 0 x t + (1/2) x 2 x t^2`
`Distance covered by the car = t^2`
**Equating the Distances:**
- Since the boy and the car are at the same distance from the starting point when the boy catches the car, we can equate their distances:
`V x t = t^2`
- Simplifying the equation:
`V = t`
Now, we need to find the value of V when the boy catches the car. To do this, we can substitute the value of t from the equation V = t into the equation V x t = t^2.
- Substituting V = t into V x t = t^2:
`t x t = t^2`
- Simplifying the equation:
`t^2 = t^2`
Therefore, the value of V can be any value as long as the time taken by the boy to catch the car is the same as the distance covered by the car. In this case, V could be any positive value, and the boy will be able to catch the car.
To find the value of V at which the boy will be able to catch the car, we need to determine the condition when the boy's distance from the starting point is equal to the car's distance from the starting point.
Let's analyze the motion of both the boy and the car separately.
**Motion of the Boy:**
- The boy starts running with a constant velocity V towards the car.
- The distance covered by the boy can be represented as:
`Distance covered by the boy = Velocity of the boy x Time taken by the boy`
- Let's assume the time taken by the boy to catch the car is t. Therefore, the distance covered by the boy can be written as:
`Distance covered by the boy = V x t`
**Motion of the Car:**
- The car starts from rest and has a constant acceleration of 2 m/sec^2 away from the man.
- The distance covered by the car can be represented using the equation of motion:
`Distance covered by the car = Initial velocity x Time + (1/2) x Acceleration x Time^2`
- Since the car starts from rest, the initial velocity of the car is 0.
`Distance covered by the car = 0 x t + (1/2) x 2 x t^2`
`Distance covered by the car = t^2`
**Equating the Distances:**
- Since the boy and the car are at the same distance from the starting point when the boy catches the car, we can equate their distances:
`V x t = t^2`
- Simplifying the equation:
`V = t`
Now, we need to find the value of V when the boy catches the car. To do this, we can substitute the value of t from the equation V = t into the equation V x t = t^2.
- Substituting V = t into V x t = t^2:
`t x t = t^2`
- Simplifying the equation:
`t^2 = t^2`
Therefore, the value of V can be any value as long as the time taken by the boy to catch the car is the same as the distance covered by the car. In this case, V could be any positive value, and the boy will be able to catch the car.
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A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car?
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A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car?.
A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy starts running with a constant velocity V towards a car which is 100m ahead of him. The car starts from rest with constant acceleration of 2m/sec sq(away from man) at the same time when man starts running towards it. For what value of V will the boy be able to catch the car?.
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