In this video, I go over the physics of a ball rolling off a table and determine how far it falls, the angle and speed it bounces with, and the distance it travels for a second bounce after losing 80% of its energy upon impact. I first obtain the position vector of the falling ball by taking integrals of the acceleration and velocity vectors. Then I determine the time until it reaches the ground, which allows obtaining the distance traveled. The slope of impact is just the derivative, thus we can then use trigonometry to obtain the angle it bounces with. Finally, I use the distance formula of projectile motion from my earlier video to find the distance of the second bounce, and thus the total distance the ball travels.
Notes - 3Speak - YouTube - Telegram - Problems Plus - mes.fm/math
#math #calculus #projectilemotion #vectors #vectorfunctions
Timestamps
- Problem 3: Ball rolls off a table and bounces – 0:00
- Solution to (a): Point at which the ball hits the floor – 1:23
- Obtain position vector from the integral of the velocity and acceleration vectors – 6:16
- The ball bounces 0.93 feet from the table – 10:07
- Velocity vectors at impact – 12:59
- Speed at impact is 15 ft/s – 14:54
- Solution to (b): Find the angle the ball bounces at – 16:41
- Derivative is the slope at the impact – 19:07
- Angle is approximately 7.6° – 23:58
- Solution to (c): Where does the 2nd bounce land after losing 80% of its speed – 26:38
- Recall the distance formula that a projectile lands from my earlier video – 30:59
- Distance of the second bounce is approximately 1.194 ft – 32:30
- Total distance the ball has traveled in 2 bounces is about 2.13 ft – 33:13
MES: https://mes.fm
Donate: https://mes.fm/donate
MES Truth: https://youtube.com/@mestruth
Hive: @mes
Email me: [email protected]