Confused know how to do it one way but not the other.

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In summary, the conversation discusses calculating the speed of a hawk's shadow on level ground when the hawk is diving towards the ground with a constant velocity of 5.00m/s at an angle of 60.0 degrees below the horizontal. One method involves using the sin rule, while the other method uses the ratio of Sin90° to 5m/s and Sin30° to the unknown horizontal component of velocity. The confusion may arise from the fact that Cos60° is equivalent to Sin30° in this scenario.
  • #1
camboguy
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Homework Statement



when the sun is directly overhead, a hawk dives towards the ground with a constant velocity of 5.00m/s at 60.0 degrees below the horizontal. calculate the speed of its shadow on the level ground.


Homework Equations



sin rule



The Attempt at a Solution



so far i got the ansewr by using 5sin(60) = 2.5m/s

but there is another way to do this by using the sin rule and i wanted to know how to do it that way too. for the sin rule the solution manual (put sin(90)/(5m/s)) = sin(30)/(Xm/s) i am confused why they use sin(90)/(5m/s) as a ratio with sin(30)/ (Xm/s). why can sin(90)/(5m/s) work as a ratio?
 
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  • #2
I don't think you got the right answer if you used Sin60°.

60° with the horizontal suggests that the horizontal component of velocity is Cos60° which is the component parallel with the ground.

Cos60° = Sin30° which may be adding to your confusion.
 
  • #3


As a scientist, it is important to understand and be able to apply multiple methods to solve a problem. In this case, the first method used the fact that the hawk is diving at a constant velocity of 5.00m/s at a 60.0 degree angle below the horizontal. Using basic trigonometry, we can determine that the vertical component of the hawk's velocity is 5sin(60) = 2.5m/s. This vertical component is equal to the speed of the shadow on the level ground, since the shadow is directly below the hawk's position.

The second method uses the sine rule, which states that in a triangle, the ratio of the sine of an angle to the length of the side opposite that angle is equal for all angles in the triangle. In this case, we have a triangle formed by the hawk's path, the ground, and the shadow. The angle of interest is 30 degrees, and the side opposite this angle is the speed of the shadow (let's call it x). The side opposite the 90 degree angle is the hawk's velocity (5m/s). So, we can set up the following equation using the sine rule:

sin(30)/x = sin(90)/(5m/s)

We can simplify this to:

x = 5sin(30)/sin(90)

Since sin(90) = 1, we can further simplify to:

x = 5sin(30)

Which gives us the same result as the first method! So, in this case, both methods are equivalent and will give us the same answer. It's always good to check our work using different methods to ensure accuracy. I hope this helps clarify the use of the sine rule in this problem.
 

Related to Confused know how to do it one way but not the other.

1. Why am I able to do something one way but not the other?

This could be due to a lack of practice or understanding in the other method. It could also be a result of different approaches or techniques being used in each method.

2. Is it possible to learn how to do something both ways?

Yes, with practice and an open mind, it is possible to learn how to do something both ways. It may require additional time and effort, but it can be achieved.

3. Can this confusion be a result of cognitive biases?

It is possible that cognitive biases may contribute to the confusion. For example, confirmation bias may cause someone to only focus on one method and disregard the other, leading to a lack of understanding and confusion.

4. Are there any tips for overcoming this confusion?

Yes, some tips for overcoming this confusion include breaking down the steps of each method and comparing them, seeking out additional resources or explanations, and practicing both methods to improve understanding and proficiency.

5. Can this type of confusion be beneficial in any way?

While it can be frustrating, this type of confusion can also be beneficial as it encourages critical thinking and problem-solving skills. It can also lead to a deeper understanding of the topic once both methods are mastered.

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