Find Initial Angle to Hit Target 100m Away with Rifle at 30deg Angle

  • Thread starter Crebble32
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In summary, to hit a target on a wall 100 m away with a rifle shooting at 300 m/s and creating a 30 degree angle with the horizon, the rifle needs to be directed at an initial angle of θ-α. The height of the target is 57.75 m and the hypotenuse is 115.5 m. Using kinematic equations, the time of flight is 0.33 seconds and the range along the inclined plane is 115.5 m. The angle of inclination α is given and θ can be found using the given values.
  • #1
Crebble32
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A rifle fires a bullet at 300 m/s at a target that is up on a wall 100 m away. The rifle's line of sight creates a 30 degree angle with the horizon. What initial angle does the rifle need to be directed to hit the target?

The formulas I thought I needed are:

Vy=ViSIN(30) Here my Vi is the V-"not"
Vx=ViCOS(30)

I found that the height of the target is 57.75 m, and the hypotenuse is 115.5 m...

I was told to find time then use a kinematic equation. So I found t=.33. I came up with several different angles in several dfferent ways and they are all too large... My prof said that it is only raised a very little bit. I have had MANY failed attempts at this and just can't figure it out.

I appreciate any help possible!
 
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  • #2
Whenever solving problem for inclined plane, consider axis along the inclined plane as x-axis and perpendicular to it as y-axis. Then
Vi(x) = Vi*cos(θ-α)
a(x) = -gsin(α)
Vi(y) = Vi*sin(θ-α)
a(y) = -gcos(α) where α is the angle of inclination and θ is the angle of projection along the horizontal.
Now proceed as usual in the projectile motion.
 
Last edited:
  • #3
I am just working in circles... just come up with the values I'm already given. I don't understand what formulas to use...
 
  • #4
Time of flight T = 2vsin(θ-α)/gcosα
Horizontal displacement OX = vcosθ *T
Range along the inclined plane = R' = OX/cosα.
Angle of inclination α is given. Now find θ.
 
  • #5
Thank you so much for your help! I think I finally got it :)
 

Related to Find Initial Angle to Hit Target 100m Away with Rifle at 30deg Angle

1. What factors affect the initial angle needed to hit a target 100m away with a rifle at a 30 degree angle?

The initial angle needed to hit a target 100m away with a rifle at a 30 degree angle is affected by the muzzle velocity of the rifle, the gravitational acceleration, and the air resistance. The muzzle velocity determines the speed at which the bullet is traveling, the gravitational acceleration affects the downward pull on the bullet, and air resistance slows down the bullet as it travels through the air.

2. How can I calculate the initial angle needed to hit a target 100m away with a rifle at a 30 degree angle?

The initial angle can be calculated using the equation: θ = tan^-1((v^2 ± √(v^4-g(gx^2+2yv^2))/(gx)) where θ is the initial angle, v is the muzzle velocity, g is the gravitational acceleration, and x and y are the horizontal and vertical distances to the target respectively. However, this equation assumes no air resistance, so it may not be entirely accurate.

3. Is it possible to hit a target 100m away with a rifle at a 30 degree angle if there is air resistance?

Yes, it is possible to hit a target 100m away with a rifle at a 30 degree angle even with air resistance. However, the initial angle needed will be slightly different than the one calculated without taking air resistance into account. To calculate the initial angle with air resistance, more complex equations and numerical methods may be needed.

4. How does the weight of the bullet affect the initial angle needed to hit a target 100m away with a rifle at a 30 degree angle?

The weight of the bullet does not have a significant effect on the initial angle needed to hit a target 100m away with a rifle at a 30 degree angle. The main factor that determines the initial angle is the muzzle velocity of the rifle. A heavier bullet may experience slightly more air resistance, but this effect is negligible for short distances like 100m.

5. Are there any other factors that may affect the initial angle needed to hit a target 100m away with a rifle at a 30 degree angle?

Other factors that may affect the initial angle needed include the wind speed and direction, the temperature and humidity, and the altitude of the shooting location. These factors can all impact the flight of the bullet and may need to be taken into consideration when calculating the initial angle. Additionally, the skill and accuracy of the shooter can also affect the accuracy of hitting the target at a specific angle.

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