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.
Returning to Take-off Velocities
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.
Problems For You To Practice On:
1. Try to calculate the vertical velocity of this jump.
Known Variables: A person has a running jump from the ground with a resultant vector speed of 10 m/s and his angle off of the ground was 45 degrees.
Vertical velocity is:______________
2. Calculate the vertical velocity of this jump.
Known Variables: A person has a running jump from the ground with a resultant vector speed of 7 m/s and his angle off of the ground was 35 degrees.
Vertical velocity is: ______________
In the third and fourth scenarios, the vertical and horizontal velocities are given. See if you can calculate the take-off velocity and angle.
3. What is the take-off velocity if and velocity are given. The vertical velocity is 6 m/s and the horizontal velocity is 6 m/s, What is the resultant velocity (take-off velocity) and angle?
3. Take-off velocity?__________________
4. Angle of take-off? __________________
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.
Answers
1. 7.1 m/s
2. 4.1 m/s
3. 8.5 m/s
4. 45 degrees