My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

Physics Physics Forum


Reply
 
LinkBack Thread Tools Display Modes
March 12th, 2018, 09:23 PM   #1
Senior Member
 
Monox D. I-Fly's Avatar
 
Joined: Nov 2010
From: Indonesia

Posts: 1,951
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.
Monox D. I-Fly is offline  
 
March 13th, 2018, 02:23 PM   #2
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,750
Thanks: 1400

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 $v_0 \approx 25.7 \, m/s$
skeeter is offline  
March 13th, 2018, 04:03 PM   #3
Senior Member
 
Monox D. I-Fly's Avatar
 
Joined: Nov 2010
From: Indonesia

Posts: 1,951
Thanks: 132

Math Focus: Trigonometry
I see. Damn physics, it's kinda hard to get an integer answer...
Monox D. I-Fly is offline  
March 30th, 2018, 12:26 PM   #4
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,159
Thanks: 866

That's because integers aren't physical!
Country Boy is offline  
March 31st, 2018, 04:10 PM   #5
Senior Member
 
Monox D. I-Fly's Avatar
 
Joined: Nov 2010
From: Indonesia

Posts: 1,951
Thanks: 132

Math Focus: Trigonometry
Quote:
Originally Posted by Country Boy View Post
That's because integers aren't physical!
Wait, what?
Monox D. I-Fly is offline  
Reply

  My Math Forum > Science Forums > Physics

Tags
bird, shot



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Scope or shot Loren Applied Math 2 June 4th, 2016 08:00 PM
Another shot in the dark Carl James Mesaros Physics 5 February 1st, 2016 07:09 AM
Not sure if this belongs here but i'll give it a shot Canadianmath Linear Algebra 2 September 13th, 2012 10:30 PM
Angry Bird rnck Physics 3 August 12th, 2011 08:47 AM
Give this one a shot?? titans4ever0927 Calculus 1 March 24th, 2009 06:08 AM





Copyright © 2018 My Math Forum. All rights reserved.