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In: Physics

A person holds a rifle horizontally and fires at a target. The bullet has a muzzle...

A person holds a rifle horizontally and fires at a target. The bullet has a muzzle speed of 200m/s and the person hears the bullet strike the target 1.00s after firing it. The air temp is 72 degrees Fahrenheit. What is the distance to the target?

Solutions

Expert Solution

The temperature is for the speed of sound in this case which is 340 m/sec at 72 F (searched from google). Actually the total time (1 sec) is the time required by the bullet to reach the target (strike the target and make a sound) plus the time required by the sound to reach back to the person.

Speed of bullet = vb = 200 m/sec
Speed of sound = vs = 340 m/sec
Distance travelled by both = S = ? (it is same for both)
time taken by bullet = tb
time taken by sound = ts

By the conditions of the question:
tb + ts = 1 => tb = 1 - ts
and
tb x vb = ts x vs = S
putting values
(1 - ts) x 200 = ts x 340
200 - 200ts = 340ts
200 = 340ts + 200ts
200 = 540ts
ts = 200/540 = 0.37037 sec
tb = 1 - 0.37037 = 0.62963 sec

S = vb x tb = 200 x 0.62963 = 125.93 m
S = vs x ts = 340 x 0.37037 = 125.93 m

Therefore, the distance between the target and the person is 125.93 meters.

genius_generous answered 2 years ago
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