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

[camboguy]

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?

 

[LowlyPion]

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.

 

[nlightner]

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.