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

Feb 22

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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.

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.