Kinematics - Acceleration in Two Dimensions. Stuck.

AI Thread Summary
The discussion centers on a physics problem involving the acceleration of a hockey puck rebounding from a board. The user is struggling with calculations for average acceleration and has attempted various methods, including the cosine law and vector components, but consistently arrives at incorrect results. Key issues identified include mixing sine and cosine in calculations, leading to confusion in determining the correct vector components. The user seeks clarification on the proper approach to resolve the problem and expresses confusion over textbook examples. Overall, the thread highlights common challenges in understanding kinematics in two dimensions.
mattstjean
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Hi, I am also having trouble with the hockey puck question.

A hockey puck rebounds from a board as shown in my diagram. The puck is in contact with the board for 2.5 ms. Determine avg acceleration of the puck over the interval.

Vi = 26 m/s Vf = 21 m/s

I tried the cosine law but I keep getting 44 m/s and not 18. I don't understand how you guys got 18 m/s. I've plugged it in at least 100 times as
<br /> v_t = \sqrt{v_1^2 + v_2^2 - 2(v_1)(v_2)cos136}<br /> = \sqrt{26^2 + 21^2 - 2(26)(21)cos136}<br /> =44<br /> =

Because that wasn't working I then tried Vector Components and I can't get that to work either. I did:
<br /> V_x = V_B sin \theta + (-V_A cos \beta ) <br /> = 21 sin(22) - 26 cos(22)<br /> =-16<br />

and

<br /> V_y = V_B cos \theta + (-V_A sin \beta ) <br /> = 21 (cos22) + 26(sin22)<br /> = 29 <br />

I then tried to figure out
<br /> \Delta V ^2= \Delta V_x ^2 + \Delta V_y^2 <br /> = sqrt{16^2 + 29^2}<br /> = 33<br />

Using that I tried to get the average acceleration by:

<br /> A_av = \Delta V / \Delta T<br /> <br /> A_av = 33 / 2.5x10^-3<br /> A_av = 13.2x10^3<br />
and to find the angle I tried to do :

<br /> \phi = tan^-1 = 16/29<br /> \phi = 29degrees<br />

However, the answer in my book says that the average acceleration is 7.3x10^3 [7.5degrees North of West]
Any help would be amazingly appreciated. Thanks.
 

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mattstjean said:
Because that wasn't working I then tried Vector Components and I can't get that to work either. I did:
<br /> V_x = V_B sin \theta + (-V_A cos \beta ) <br /> = 21 sin(22) - 26 cos(22)<br /> =-16<br />
You have a mix of sine and cosine. Only one is correct.
and

<br /> V_y = V_B cos \theta + (-V_A sin \beta ) <br /> = 21 (cos22) + 26(sin22)<br /> = 29 <br />
Again, a mix of sine and cosine.

Redo this.
 
Doc Al said:
You have a mix of sine and cosine. Only one is correct.

Again, a mix of sine and cosine.

Redo this.

I don't know how to redo it. In my textbook it used them both together in the y and x component vector subtraction. I took the equations right out of my text, Nelson Physics 12.
 
mattstjean said:
I don't know how to redo it. In my textbook it used them both together in the y and x component vector subtraction. I took the equations right out of my text, Nelson Physics 12.
I'm not sure what equations you are talking about.

Do this: What's the x-component of Vi? The x-component of Vf?
 
I have the same book and I am stuck on the example on right before the quesion box you asked about. can you please explain the lawn mower example in pg 28. I AM VERY CONFUSED
 
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