Distance

[Guest]

A bullet is fired at a target and 2 seconds later the bullet is heard striking the target.

Speed of bullet- 2500 feet per second.

Speed of sound- 1100 fps.

Calculate distance to target.

Thanks for assistance.

[Guest]

....Is this a hypo-thetical.....question
It depends how far the listener is away from the target......or does it...??
I'll assume the listener is same distance from target as "shooter"
I'll assume he is not the "shooter" because if he had ear muffs on he wouldn't hear the bullet hitting the target anyway.
If he didn't have ear muffs on he would be deafened by the "bang" from the gun and wouldn't hear it either.
But....Ill assume he is somewhere along a circle at a radius "d" same distance as "shooter".....but not diagonally opposite as the bullet may pass through the target and shoot him.....so in that case he wouldn't hear it either.

Distance travelled by bullet is same as distance travelled by sound.
Distance = velocity x time

Bullet distance is 2500 x TB
Sound Distance is 1100 x TS

Also TB + TS = 2
so TB = 2 - TS

1100 x TS = 2500 x ( 2 - TS )

1100 x TS = 5000 - 2500 x TS

3600 x TS = 5000

TS = 5000 / 3600 = 25 / 18 = 1 7/18 Secs

TB = 11/18 Secs

Distance (d) = 2500 x 11 / 18 = 1527.78 feet

............Simple

But..... the speeds are the ratio of 11 to 25.
gives 36 parts altogether to travel 2d in the total time of 2 secs .......to the target and back
So bullet part is (11 / 36) of 2 secs.....equals 11/18 secs
Distance = velocity x time = 2500 x (11/18) = 1527.78 feet

.........Simple

[Guest]

I found the problem in a first year college math book from the 1940's.

How did you calculate this in the first part of the solution?

TB = 11/18 Secs


Thanks.

[Guest]

The first part is by using simultaneous equations....I probably should have used a few brackets to make it more readable

TB is the time taken for the bullet to travel from the gun to the target
TS is the time taken for the sound made my hitting the target to travell to the listener.
We are told the total time is 2 seconds from trigger is pulled until the target sound is heard.
So...... TB plus TS totals 2 seconds..... TB + TS = 2 .......Eqn (1)
Re-arranging gives....... TB = (2 - TS)

Also from question I am assumed the listener was at the same distance from the target as was the shooter.
Distance travelled is Speed multiplied by time taken.

Distance travelled by bullet equals Distance travelled by the sound

1100 x TS = 2500 x TB ..........Eqn (2)
But....from above ..... TB = (2 - TS)....and substituting in eqn 2.......

So......1100 x TS = 2500 x (2 - TS)

...... (1100 x TS) = 5000 - (2500 x TS) ........working out the brackets..

......... (3600 x TS) = 5000 ......collecting like terms...

So........TS = ( 5000 / 3600 )

and..... TS = ( 25 / 18 ) Seconds .....cancelling down the big numbers....

gives TS = 1 7/18 Seconds.....This reads " one and seven eighteenths seconds"

and as Total time is 2 seconds TB = (2 - TS)....gives.....(2 minus ( 1 7/18 ) = ( 11/18 ) seconds

So distance from gun to target is 2500 x ( 11/18 ) = 1527.78 feet.

.........I then realised I didn't need to do it this long-winded way and did it again by ratio of the speeds...

[Bigboss01]

So the actual overall width will be the width of the shelves plus the thickness of the two uprights...
We don't know the thickness of the wood.