Triangle calculation for the resultant velocity

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
 
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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) ##
 
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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?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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