Mastering Motion of 2 Dimensions in Physics - Solved Problem and Techniques

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SUMMARY

The discussion focuses on solving two-dimensional motion problems in Grade 12 Advanced Placement Physics using the Component Technique. A specific problem is presented where a ball is thrown from a hot-air balloon, and the goal is to determine its initial velocity given its acceleration and final velocity after 2 seconds. The solution involves calculating horizontal and vertical components of velocity, leading to an initial speed of 17.17 m/s. Key formulas used include Vx^2 + Vy^2 = 24^2 and the relationship between initial and final velocities in projectile motion.

PREREQUISITES
  • Understanding of kinematics in two dimensions
  • Familiarity with the Component Technique for vector resolution
  • Knowledge of basic trigonometry, specifically sine and cosine laws
  • Ability to apply equations of motion, such as acceleration and velocity calculations
NEXT STEPS
  • Study the Component Technique in-depth for solving projectile motion problems
  • Learn how to derive initial velocities from final velocities in two-dimensional motion
  • Practice additional problems involving acceleration and angle calculations in projectile motion
  • Explore the effects of air resistance on projectile motion for a comprehensive understanding
USEFUL FOR

This discussion is beneficial for Grade 12 Advanced Placement Physics students, educators teaching kinematics, and anyone looking to master the concepts of two-dimensional motion and projectile analysis.

deliveryman
[SOLVED] Physics - HELP!

Hey guys,

Currently taking Grade 12 Advanced Placement Physics. I'm craming for a kinetics test tomorrow, which I will do reasonably well. However, I am still stumped on solving Motion of 2 Dimensions using the "Component Technique". I am able solve it using the Sine and Cosine laws, but I have to be able to solve it using both.

If anyone could help me out by taking a shot at explaining it, it would be very much appreicated.

A sample problem:

A passenger in a hot-air balloon throws a ball with an initial unknown velocity. The ball accelerates at 9.8m/s/s [down] for 2.0s, at which time its instantaneious velocity is 24m/s [45 degrees below the horizontal]. Determine the ball's initial velocity.

Again, any help would be greatly appreciated.
 
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After 2 seconds,
Vx^2 + Vy^2 = 24^2

With the 45 degree angle thing, conclude Vx = Vy at this time

Vx = (576/2)^0.5
= 16.97ms-1
Vy = 16.97ms-1

Assume horizontal velocity unchanged over 2s. Ux = Vx = 16.97ms-1

Uy = Vy - 9.81*2
= - 2.63ms-1

Note: 'U' refers to initial velocities, 'V' to end ones, 'x' to horizontal direction, 'y' to vertical.

Initial speed = 17.17ms-1
 

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