Triangle calculation for the resultant velocity

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SUMMARY

The resultant velocity of 31.7 m/s is calculated using the Pythagorean theorem, specifically through the equation 31.748 = √(30.8² + 7.7²), where 30.8 m/s is the horizontal component and 7.7 m/s is the vertical component of the velocity. The angle of 14 degrees, calculated using the formula 14.03 = (180/π) * atan2(7.7, 30.8), represents the angle off the horizontal that these two velocities create. This discussion clarifies the method for determining the resultant velocity and its direction in two-dimensional motion.

PREREQUISITES
  • Understanding of the Pythagorean theorem
  • Familiarity with trigonometric functions, specifically atan2
  • Basic knowledge of vector resolution in two dimensions
  • Ability to perform calculations involving angles and velocities
NEXT STEPS
  • Study vector addition and resolution techniques in physics
  • Learn about the application of trigonometric functions in physics problems
  • Explore the concept of resultant vectors in two-dimensional motion
  • Practice calculating angles and magnitudes of resultant velocities using different examples
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Students studying physics, engineers working with motion analysis, and anyone interested in understanding vector resolution and resultant velocity calculations.

DeanH87
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Homework Statement
Hi, Can someone help with the below calculation. Sample attached
Relevant Equations
See Below
1591845692283.png
Top example- How do I get to 31.7 m/s from 30.8 and 7.7? This is way over my head and need help. Thanks in advance
Dean
 
Last edited by a moderator:
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##31.748 = \sqrt { 30.8^2 + 7.7^2 }##
It is the length of the hypotenuse of the right triangle formed by the horizontal and vertical numbers.
And the 14 deg is the angle off of horizontal that those two velocities make for the combined velocity.
## 14.03 = (180/\pi) * atan2(7.7, 30.8) ##
 
Last edited:
Great! Thanks
 
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DeanH87 said:
Homework Statement:: Hi, Can someone help with the below calculation. Sample attached
Relevant Equations:: See Below

View attachment 264461Top example- How do I get to 31.7 m/s from 30.8 and 7.7? This is way over my head and need help. Thanks in advance
Dean
What do you know about resolving forces in 2 dimensions?
 

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