Question

How do I find the angle of elevation given total distance and velocity?

Answer 1

To find the angle of elevation given the total distance and velocity, you can use the equations of projectile motion. The angle of elevation refers to the angle at which an object is launched or projected upwards.

Here's a step-by-step approach to finding the angle of elevation:

1. Determine the horizontal distance (range) covered by the projectile. This is the total distance given in the problem.

2. Determine the vertical distance (height) covered by the projectile. If the object is launched and lands at the same height, then the vertical distance would be zero.

3. Calculate the time of flight (duration) of the projectile. This can be done using the following formula:

   • t = (2 * V * sin(theta)) / g

   where:

   • t is the time of flight,
   • V is the initial velocity of the projectile,
   • theta is the angle of elevation,
   • g is the acceleration due to gravity (approximately 9.8 m/s^2).

4. Use the time of flight to calculate the vertical distance covered by the projectile using the following formula:

   • h = (V^2 * sin^2(theta)) / (2 * g)

   where h is the vertical distance.

5. Now, you have the vertical distance and the horizontal distance. You can use trigonometry to find the angle of elevation:

   • tan(theta) = h / R

   where R is the horizontal distance (range).

6. Solve the equation for theta to find the angle of elevation:

   • theta = arctan(h / R)

   Note: Depending on your calculator or programming language, the inverse tangent function may be denoted as "atan" or "arctan."

By following these steps, you can determine the angle of elevation given the total distance and velocity of a projectile.