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# Bullet Trajectory Question, appreciate any help.

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A bullet hole is 80" (inches) from the floor against a wall.

A shoe print from the shooter is 45" away from the wall.

The bullet was shot from a 65 degree angle.

What is the shooter's shoulder height? (from where he fired the gun)

Guest Mar 11, 2017
edited by Guest  Mar 11, 2017

#6
+10657
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Nice job completing the puzzle Hecticar !     The PROBLEM wasn't that difficult, but the erroneous presentation (which you figured out) was !        Keep up the good work !!

ElectricPavlov  Mar 11, 2017
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#1
+5552
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The shooters height will be (80 + x) inches

The third angle in the triangle is 180 - 90 - 65 = 25º

tan25º = x/45

45tan25º = x

Shooter's height = 80 + 45tan25 ≈ 100.984 inches

That is over 8 feet tall!

Okay I just figured out that it probably means this:

In which case the height is 80 - 45tan25 ≈ 59.016 inches

About 4.9 feet, which makes more sense.

hectictar  Mar 11, 2017
edited by hectictar  Mar 11, 2017
edited by hectictar  Mar 11, 2017
#2
+5

Hey hectictar, thanks for responding.

I may have explained this poorly. The shooter is not 100 inches tall, heh.

The wall is X inches tall. The bullet hole is in the wall at 80 inches up.

The shooter shot from 45 inches away.

He shot UPWARDS at 65 degrees. It's not like he was pointing the gun straight at the wall.

Guest Mar 11, 2017
edited by Guest  Mar 11, 2017
#3
+10657
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I cannot get these numbers to work...... are you sure you have them correct???

From 45 inches away a 65 degree angle would put the bullet at

tan 65 = opp/adj = opp/45

45 tan 65 = 96 inches ABOVE shoulder height and the hole is only 80 inches above the floor....which would mean his shoulder was 16 inches BELOW the floor.....

ElectricPavlov  Mar 11, 2017
#4
+10657
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If we assume the bullet travels in a straight line (it doesn't) we do not need to know the muzzle velocity.

Let's assume the shot is UPWARD at a 6. 5 degree angle

tan 6.5 = opp/45    opp = 5.127 "

80-5.127 = 74 inch shoulder height (pretty tall  people are usually about 7-8 heads tall ...this person would be ~~86 inches tall ....IF the angle is 6.5 degrees upward)

ElectricPavlov  Mar 11, 2017
#5
+5552
+6

I actually drew the second picture wrong. I think the confusion is over whether the 65º angle is from vertical or horizontal. This is how the second one I did should look like:

I was making it really fast so I messed up.

But when it's like this the height actually is 80 - 45tan25º ≈ 59.016 inches

hectictar  Mar 11, 2017
#6
+10657
+10

Nice job completing the puzzle Hecticar !     The PROBLEM wasn't that difficult, but the erroneous presentation (which you figured out) was !        Keep up the good work !!

ElectricPavlov  Mar 11, 2017

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