Physics projectile motion / vertical circular motion question?

Https://www.flickr.com/photos/61682497@N... I've redrawn this to make the angle look more like 40º and to put the initial velocity on the x-axis. Then, using unit vectors I and j, we can write initial v = v I final v = vcos40 I + vsin40 j The change in velocity is the difference:? V = final v - initial v = v(cos40 - 1) I + vsin40 j which has magnitude?

V| = v *?(cos40 - 1)² + sin²40 = v *? Cos²40 - 2cos40 + 1 + sin²40 and since cos²40 + sin²40 = 1, we have? V| = v *?(2 - 2cos40) = v *?2(1 - cos40) Because you've supplied an answer, I know that we need a half-angle formula: use 2sin²?

= 1 - cos(2?)? See citation, look for "power reducing/half angle formulas" Here, then, we have 1 - cos(2*20) = 2sin²20, and substituting in gives? V| = v *?2(2sin²20) = v *?(4sin²20) and finally?

V| = v * 2sin20 = 2vsin20 Boom.

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