Now that you are familiar with separating the take-off velocity into vertical and horizontal components, and vice versa, there is an easy mathematical formulae to calculate the actual magnitudes of these velocities.
These formulas come from the fact that the take-off, vertical, and horizontal velocities form a right triangle. Whenever you have a right triangle, you can use sine, cosine, and tangent to calculate one side of the triangle if you know an angle and another side. The following triangles displays the relationships between the sides of a triangle and an angle.
If you know the take-off velocity and angle, you can then draw the vertical and horizontal velocities, and you have your right triangle. The opposite side is the magnitude of the vertical velocity, the adjacent side is the magnitude of the horizontal velocity, and the hypotenuse is the magnitude of the take-off velocity.
The following illustration contains four different scenarios.
In the first two scenarios, the take-off angle and velocity are given. Try to calculate the vertical velocity of the skater. Click on the solution to see if you are correct.
In the third and fourth scenarios, the vertical and horizontal velocities are given. See if you can calculate the take-off velocity and angle.
Here's a hint: You can still use SOHCAHTOA.
If you can do these easily, then keep going. If you need help, then go on to this help page for an explanation of how to do these problems.
|
|
|
