A Machine Gun Is Mounted On A Tank Moving At A Speed Of 20 Ms–1towards A Target With The Gun Pointing In The Direction Of Motion Of The Tank. The Muzzle Speed Of The Bullet Equals The Speed Of Sound = 340 Ms–1. If, At The Time Of Firing, The Target Is 500 M Away From The Tank, Then  

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Question

A machine gun is mounted on a tank moving at a speed of 20 ms–1towards a target with the gun pointing in the direction of motion of the tank. The muzzle speed of the bullet equals the speed of sound = 340 ms–1. If, at the time of firing, the target is 500 m away from the tank, then  

Solution

Correct option is

The sound arrives at the target later than the bullet

 

Since only the source of sound, i.e. the gun is in motion, the speed of sound remains unchanged at 340 ms –1. Therefore, the time taken by the sound of firing to arrive at the target 500 m away is

                       

If the gun points in the direction of motion of the tank, the effective speed of the bullet = 340 + 20 = 360 ms–1. Therefore the time taken by the bullet to reach the target is 

                     

Since ts > tb.   

Testing

SIMILAR QUESTIONS

Q1

A wire has a mass 30 g and linear density 4 × 10 –2 kg m–1. It is stretched between two rigid supports and vibrates in its fundamental mode with a frequency of 50 Hz. What is the speed of transverse waves on the wire?

Q2

A steel rod of length 1.0 m is clamped rigidly at its middle. What is the frequency of the fundamental mode for the longitudinal vibrations of the rod? The speed of sound in steel = 5 × 103 ms –1 

Q3

Two tuning forks A and B produce 10 beats per second when sounded together. On slightly loading fork A with a little wax, it was observed that 15 beats are heard per second. If the frequency of fork B is 480 Hz, what is the frequency of fork A before it was loaded?

Q4

Two sitar strings A and B are slightly out of tune and produce beats of frequency 6 Hz. When the tension in string A is slightly decreased, the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

Q5

A metal wire of diameter 1 mm is held on two knife edges separated by a distance of 50 cm. The tension in the wire is 100 N. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats per second. The tension in the wire is then reduced to 81 N. When the two are excited, beats are heard at the same rate. What is the frequency of the fork?

Q6

An ambulance blowing a siren of frequency 700 Hz is travelling slowly towards a vertical reflecting wall with a speed of 2 ms–1. The speed of sound is 350 ms–1. How many beats are heard per second?

Q7

Two persons A and B, each carrying a source of sound of frequency V, are standing a few metres apart in a quiet field. A starts moving towards Bwith a speed u. If v is the speed of sound, the number of beats heard per second by A will be

Q8

A train standing at a certain distance from a railway platform is blowing a whistle of frequency 500 Hz. If the speed of sound is 340 ms –1, the frequency and wavelength of the sound of the whistle heard by a man running towards the engine with a speed of 10 ms –1 respectively are      

Q9

A submarine is fitted with a SONAR (Sound Navigation and Ranging) system which operates at an ultrasonic frequency of 42 kHz. An enemy submarine is moving towards the SONAR with a speed of 200 ms –1. If the speed of sound in seawater is 1400 ms–1, what is the frequency of sound received back at the SONAR fitted submarine after reflection from the enemy submarine?     

Q10

 

When a wave travels in a medium, the particle displacement are given by   

                           

Where ab and c are constants. The maximum particle velocity will be twice the wave velocity if