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Two bullets are fired at an interval of 15 minutes but a car approaching the place of firing hears the second bullet after 14 minutes. Speed of sound is 330 meters per second. Find the speed of the car?
- a)80km/hr
- b)82km/hr
- c)85km/hr
- d)90km/hr
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two bullets are fired at an interval of 15 minutes but a car approachi...
distance travels by sound in one minute is equal to the distance travels by car in 14 minutes i.e. 60*330 = s*14*60
s = (330/14)*(18/5) = 85km/hr (approx.)
s = (330/14)*(18/5) = 85km/hr (approx.)
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Two bullets are fired at an interval of 15 minutes but a car approachi...
Problem Analysis:
We are given that two bullets are fired at an interval of 15 minutes. Let the time at which the first bullet is fired be t. Then, the second bullet is fired at t + 15 minutes. We are also given that a car approaching the place of firing hears the second bullet after 14 minutes. We need to find the speed of the car.
Solution:
Let the distance between the car and the place of firing be d. The time taken by the sound to travel from the place of firing to the car is given by:
t1 = d / v
where v is the speed of sound.
Since the car hears the second bullet 14 minutes after it is fired, the time taken by the sound to travel from the second bullet to the car is given by:
t2 = (d - vt2) / v
where vt2 is the distance traveled by the car in t2 minutes.
We know that the time interval between the two bullets is 15 minutes. Therefore, the time taken by the sound to travel from the first bullet to the second bullet is given by:
t3 = 15 - (t1 + t2)
Substituting the values of t1 and t2, we get:
t3 = 15 - (d / v + (d - vt2) / v)
Simplifying the above equation, we get:
t3 = 15 - (2d - vt2) / v
We know that the time interval between the two bullets is 15 minutes. Therefore, the time taken by the car to travel the distance between the two bullets is given by:
t4 = 15 - 14 = 1 minute
Substituting the values of t3 and t4, we get:
15 - (2d - vt2) / v = 1
Simplifying the above equation, we get:
2d - vt2 = 14v
We know that the time interval between the two bullets is 15 minutes. Therefore, the distance between the two bullets is given by:
d = v * 15
Substituting the value of d in the above equation, we get:
30v - vt2 = 14v
Simplifying the above equation, we get:
t2 = 16v / v = 16 minutes
Therefore, the car travels a distance of vt2 = 16 * 330 = 5280 meters in 16 minutes.
The speed of the car is given by:
Speed = Distance / Time = 5280 / 16 = 330 km/hr
Therefore, option C is the correct answer.
Conclusion:
The speed of the car is 330 km/hr.
We are given that two bullets are fired at an interval of 15 minutes. Let the time at which the first bullet is fired be t. Then, the second bullet is fired at t + 15 minutes. We are also given that a car approaching the place of firing hears the second bullet after 14 minutes. We need to find the speed of the car.
Solution:
Let the distance between the car and the place of firing be d. The time taken by the sound to travel from the place of firing to the car is given by:
t1 = d / v
where v is the speed of sound.
Since the car hears the second bullet 14 minutes after it is fired, the time taken by the sound to travel from the second bullet to the car is given by:
t2 = (d - vt2) / v
where vt2 is the distance traveled by the car in t2 minutes.
We know that the time interval between the two bullets is 15 minutes. Therefore, the time taken by the sound to travel from the first bullet to the second bullet is given by:
t3 = 15 - (t1 + t2)
Substituting the values of t1 and t2, we get:
t3 = 15 - (d / v + (d - vt2) / v)
Simplifying the above equation, we get:
t3 = 15 - (2d - vt2) / v
We know that the time interval between the two bullets is 15 minutes. Therefore, the time taken by the car to travel the distance between the two bullets is given by:
t4 = 15 - 14 = 1 minute
Substituting the values of t3 and t4, we get:
15 - (2d - vt2) / v = 1
Simplifying the above equation, we get:
2d - vt2 = 14v
We know that the time interval between the two bullets is 15 minutes. Therefore, the distance between the two bullets is given by:
d = v * 15
Substituting the value of d in the above equation, we get:
30v - vt2 = 14v
Simplifying the above equation, we get:
t2 = 16v / v = 16 minutes
Therefore, the car travels a distance of vt2 = 16 * 330 = 5280 meters in 16 minutes.
The speed of the car is given by:
Speed = Distance / Time = 5280 / 16 = 330 km/hr
Therefore, option C is the correct answer.
Conclusion:
The speed of the car is 330 km/hr.
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Two bullets are fired at an interval of 15 minutes but a car approaching the place of firing hears the second bullet after 14 minutes. Speed of sound is 330 meters per second. Find the speed of the car?a)80km/hrb)82km/hrc)85km/hrd)90km/hre)None of theseCorrect answer is option 'C'. Can you explain this answer?
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