A projectile is fired at an angle of 60degree with the horizontal. Elevation angle of the projectile at it's highest point as seen from the point of projection is Ans is in tan function.?

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Understanding the Projectile Motion
When a projectile is fired at an angle, it follows a parabolic trajectory. The key points of interest in projectile motion include the launch angle, the maximum height, and the angle of elevation from the launch point to the highest point of the projectile's path.
Launch Angle and Maximum Height
- The projectile is launched at a 60-degree angle with respect to the horizontal.
- At the highest point, the vertical component of the velocity becomes zero, and the projectile starts descending.
Elevation Angle at the Highest Point
- To find the elevation angle from the launch point to the maximum height, we can analyze the geometry of the situation.
- At the maximum height, the horizontal distance traveled by the projectile can be denoted as 'R' (the horizontal range) while the height can be denoted as 'H.'
Using the Tangent Function
The elevation angle (θ) can be expressed using the tangent function:
- The elevation angle θ can be determined using the relation:
tan(θ) = H / R
Where:
- H = Maximum Height
- R = Horizontal Range
Key Insights
- The maximum height can be calculated using the formula: H = (v^2 * sin^2(θ)) / (2 * g), where v is the initial velocity and g is the acceleration due to gravity.
- The horizontal range R can be found using: R = (v^2 * sin(2θ)) / g.
By substituting these values into the tangent function, you can express the elevation angle in terms of the launch angle and other parameters of the projectile.
This relationship clearly shows how the angle of elevation at the highest point can be derived, emphasizing the role of the tangent function in projectile motion analysis.

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