When a projectile is fired or thrown near the surface of the earth its path is parabolic. Several students debated the pronunciation of the noun, parabola, and the adjective, parabolic.
The x and y components of a projectile's motion can be treated as two separate one-dimensional situations. The x component's velocity does not change once the projectile has been launched. The y component is gravity.
A projectile's maximum height will be reached when the y component of its velocity is zero.
If the projectile lands at the same height from which it was launched, it will reach its maximum height at the midpoint of the journey. The final value of Vy will be the negative of the initial value of Vy. In other words, the final velocity equals the initial velocity. Good examples are throwing a football to anther person, firing a cannon at a target.
To show that the y component velocity is independent of the x component we timed how long it took a rubber band to hit the floor after being shot a few feet as shown below and also by just dropping it from the same height. Two groups had times within a ten percent error, very good, and one group was repeatedly off by 30% I should have had them change timers!
In calculations remember that the Cosine of zero is 1 (one) and the Sine of zero is zero.
We looked at the range formula. Range = V^2 (initial velocity) times sin2times the angle divided by gravity. It is not important to be able to derive this formula although the derivation is in the book. You would use this formula to determine how far a projectile would fly based on initial velocity and the angle from the ground.
We made several observations from the range formula. If you double the initial velocity, the range is quadrupled as V is squared in the range equation. If you were aiming at a target and your first shot fell short, you would decrease the angle to get the projectile to go farther. Handy to know if you are firing a mortar or throwing a football.
No comments:
Post a Comment