My Math Forum [ASK] Shot Bird

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 March 12th, 2018, 10:23 PM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry [ASK] Shot Bird A bird is located at the (50, 8 ) m coordinate. A boy shot a rock at it using a slingshot with the elevation angle $\displaystyle 37^{\circ}$. How much velocity is needed for the rock to be able to hit that bird? I substituted all known variables (including the gravity acceleration $\displaystyle 10m/s^2$, with $\displaystyle \sin37^{\circ}=\frac{3}{5}$ and $\displaystyle \cos37^{\circ}=\frac{4}{5}$) to $\displaystyle x=v_0\cos\alpha t$ and $\displaystyle y=v_0\sin\alpha t-\frac{1}{2}gt^2$. Substituting the $\displaystyle v_0$ I got from both equations resulted in $\displaystyle \frac{125}{2t}=\frac{40+25t^2}{3t}$ and I got $\displaystyle t^2=5,9$. Am I right? Because if it is indeed the right value of t, everything will be complicated from there.
 March 13th, 2018, 03:23 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,815 Thanks: 1458 If the shot originates at the origin, then your solution for time is correct. You may want to try this ... $\Delta x = 50$ and $\Delta y = 8$ the idea here is to remove the parameter of time ... $\Delta x = v_0 \cos{\theta} \cdot t \implies t = \dfrac{\Delta x}{v_0 \cos{\theta}}$ substitute the above value for time in the equation $\Delta y = v_0 \sin{\theta} \cdot t - \dfrac{1}{2}gt^2$ $8 = v_0 \sin(37) \cdot \dfrac{50}{v_0 \cos(37)} - 5 \left[\dfrac{50}{v_0 \cos(37)}\right]^2$ $\sin(37) \approx \dfrac{3}{5}$ and $\cos(37) \approx \dfrac{4}{5}$ ... $8 = \dfrac{75}{2} - \dfrac{78125}{4v_0^2}$ your solution should be $v_0 \approx 25.7 \, m/s$
 March 13th, 2018, 05:03 PM #3 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry I see. Damn physics, it's kinda hard to get an integer answer...
 March 30th, 2018, 01:26 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 That's because integers aren't physical!
March 31st, 2018, 05:10 PM   #5
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Joined: Nov 2010
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Math Focus: Trigonometry
Quote:
 Originally Posted by Country Boy That's because integers aren't physical!
Wait, what?

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