# Calculating angle of projectile to hit target

• vetgirl1990
In summary, the problem involves launching a projectile from an origin on a tilted plane at a 30 degree angle with the horizontal. The ball has an initial velocity of 0.2m/s. The goal is to determine the angle at which the projectile should be launched in order to hit a target located at (0.7m, 0.6m). The equations used are r_f = r_i + v_i*t + 1/2at^2, v_y = vsinΘ, and v_x = vcosΘ. By substituting the initial velocity and target coordinates into the equations and rearranging, it is determined that the projectile should be launched at an angle of 36.87 degrees to hit the
vetgirl1990

## Homework Statement

A projectile is launched from an origin (0cm,0cm) on a tilted plane. The plane makes 30 degrees with the horizontal. The launcher sends the ball with a speed of 0.2m/s.

At what angle should the projectile be launched to hit the target at (0.7m,0.6m) location?
Assume there are no resistive forces to the projectile motion in this plane.

## Homework Equations

r_f = r_i + v_i*t + 1/2at2

Breaking the velocity vector into it's x and y components:
v_y = vsinΘ
v_x = vcosΘ

## The Attempt at a Solution

In the x-direction:
There is no acceleration in the x direction, so the above equation is reduced to:
x_f - x_i = vcosΘ*t
0.6 = vcosΘt
t = 0.3 / cosΘ (EQUATION 1)

In the y-direction:
y_f - y_i = vsinΘt - 4.9t2
0.7 = vsinΘt - 4.9t2 (EQUATION 2)

SUB EQUATION 1 INTO 2

0.7 = 0.2sinΘ (0.3/cosΘ) - 4.9(0.3/cosΘ)2
This is where I get stuck... solving the trigonometric equation. I can't find a solution, so I'm thinking that my above reasoning may be wrong.
Either that, or I am just having an incredibly hard time with trig -- which I've been out of practice for 8 years.
Any suggestions / guidance is very much appreciated.

From the description in the problem statement it sounds like the projectile is being launched in the tilted plane. If that's so you'll want to consider what the acceleration due to gravity is in the plane. It won't be 9.8 m/s2, but rather some fraction of that which depends upon the tilt of the plane to the horizontal.

For your equation 1 it looks like you've divided 0.6 by 0.2 and arrived at 0.3 (the x-displacement 0.6 m divided by the initial velocity of 0.2 m/s). You'll want to check that.

These trig equations can be tricky. Keep in mind the basic identity sin2 + cos2 = 1. If you can get everything in terms of either sin or cos then it'll boil down to algebra if you make suitable substitutions (for example: "let z = cos2(Θ)").

vetgirl1990
gneill said:
From the description in the problem statement is sounds like the projectile is being launched in the tilted plane. If that's so you'll want to consider what the acceleration due to gravity is in the plane. It won't be 9.8 m/s2, but rather some fraction of that which depends upon the tilt of the plane to the horizontal.

For your equation 1 it looks like you've divided 0.6 by 0.2 and arrived at 0.3 (the x-displacement 0.6 m divided by the initial velocity of 0.2 m/s). You'll want to check that.

These trig equations can be tricky. Keep in mind the basic identity sin2 + cos2 = 1. If you can get everything in terms of either sin or cos then it'll boil down to algebra if you make suitable substitutions (for example: "let z = cos2(Θ)").

Thank you, this helped a lot! Expressing the trig in terms of another variable was the trick at the end.

## 1. How do you calculate the angle of a projectile to hit a specific target?

The angle of a projectile can be calculated using the formula: θ = sin-1(d/(v2/g)) where θ is the angle, d is the horizontal distance to the target, v is the initial velocity of the projectile, and g is the acceleration due to gravity.

## 2. What factors affect the angle of a projectile?

The angle of a projectile is affected by the initial velocity, the horizontal distance to the target, and the acceleration due to gravity. Additionally, air resistance and wind can also affect the angle of a projectile.

## 3. How can I adjust the angle of a projectile to hit a target that is far away?

To hit a target that is far away, you can increase the initial velocity of the projectile or decrease the acceleration due to gravity. This will change the angle needed to hit the target.

## 4. Can the angle of a projectile be negative?

No, the angle of a projectile cannot be negative. It is always measured as a positive value in degrees or radians.

## 5. Is there a specific angle that will always hit a target?

No, there is not a specific angle that will always hit a target. The angle needed to hit a target depends on the initial conditions and the distance to the target. However, there is an optimal angle that will result in the maximum range for a given initial velocity.

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