Calculating Angle for Accurate Shooting

[mathcrzy]

A hunter aims directly at a target (on the same level) 130 m away.

(a) If the bullet leaves the gun at a speed of 300 m/s, by how much will it miss the target?
.9 m

(b) At what angle should the gun be aimed so the target will be hit?
_____°

 

[Loren Booda]

1. How much time does the bullet take to reach the target, assuming its speed is constant?

2. What is the gravitational acceleration acting upon the bullet over this time?

3. What is the formula for distance dropped due to constant acceleration and zero initial velocity?

4. How far does the bullet fall due to the acceleration over the time of travel?

5. Calculate the tangent for the distance fallen vs. the distance to the target.

 

[mathcrzy]

1. .43 seconds

2. 9.8m/s^2

3. ?

4. .9m in 130 m

5. ?

 

[Lemm]

Y and X components of motion here are separate things, so in number 3 u treat the bullet falling as a separate part, where a=g. (You already have T, so just look for the formula that works) basically what u did to obtain number 4, just that you write your formula and variables down for Y component of motion.

5.I believe is trigonometry, SOH,CAH,TOA. The tangent of distance fallen vs the distance travelled, is visualized much clearer if you do a diagram, you know that distance travel is a straight parallel line on the X axis, and distance fallen is a distance in the Y axis, if you draw this you will get a right triangle. There you can calculate the angle that the bullet falls, using Angle = Tan Y/X (TOA). If you know that the bullet shot at 0 degrees will fall Y distance at a X degree angle, what would happen if you shoot it at a +X angle?

(draw diagrams, it makes it much easier to visualize)

 

[mathcrzy]

i figured out the hypotenuse=130.0031153. now how do i figure out the angle?

 

[Loren Booda]

Hints:

What does at²/2 equal?

Also, remember sin(Angle)=opposite/hypotenuse.