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Feb 22

# Finding out angle of projection given only vertical and horizontal motions?

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Feb 22
To find the angle of projection given only the vertical and horizontal motions, you can use the following steps:

1. Determine the initial velocity components in the horizontal and vertical directions. This can be done by using the equations of motion:

- Horizontal motion: $$v_{0x} = v_0 \cos(\theta)$$
- Vertical motion: $$v_{0y} = v_0 \sin(\theta)$$

Where:
$$v_{0x}$$ = initial velocity in the horizontal direction
$$v_{0y}$$ = initial velocity in the vertical direction
$$v_0$$ = initial velocity of the projectile
$$\theta$$ = angle of projection

2. Use the vertical motion equation to find the time of flight ($$t$$):

$$y = v_{0y}t - \frac{1}{2}gt^2$$

Where:
$$y$$ = vertical displacement
$$g$$ = acceleration due to gravity

3. Use the horizontal motion equation to find the range ($$R$$):

$$R = v_{0x}t$$

4. Use the range and time of flight to find the angle of projection:

$$\theta = \arctan(\frac{y}{R})$$

By following these steps, you can determine the angle of projection given only the vertical and horizontal motions of the projectile.
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