How fast is the fly's shadow moving?

[goatedgolgi]

Homework Statement

A fly in a room is flying on a bearing of 204
at a speed of 0.36ms −1
. Sunlight streams horizontally westward across a room, forming a shadow of the fly on the west wall. How fast does the shadow move? Give your answer to 2 significant figures.

Relevant Equations

SOHCAHTOA

Hii! i've attempted this question and guessed which componenet of the fly's velocity would determine the shadows velocity.... apparently it's the vertical compenent but i haven't got a clue why! i used cos(66)x0.36 to get 0.15 to two s.f and sin(66)x0.36 to give 0.33ms-1 with 0.33ms-1 being the answer...

 

[PeroK]

Is there a diagram? I would have assumed from the question that the fly is flying horizontally.

 

[goatedgolgi]

Unfortunately no diagram...I have attached one i did myself.... I think i assumed so too? hence why i used cosx first

 

[PeroK]

Okay, so your question is why to use sine and not cosine? What if the bearing was 270 degrees?

 

[goatedgolgi]

Would the velocity be parallel to the sunlight? soo this means that the vertical component of the velocity is in line with the sunlight...?

 

[nasu]

Your angle marked as 66 degrees is wrong. The bearing of 204 is from north, isn't it? So, what will be the angle made with the south direction, which is a bearing of 180?

 

[goatedgolgi]

OHH wait is the angle 66 degrees meant to be between the sunlight line and the vector 0.36.. sorry about that!! for the angle made with the south direction i'm a bit confused with what u are referring to..

 

[PeroK]

OHH wait is the angle 66 degrees meant to be between the sunlight line and the vector 0.36.. sorry about that!! for the angle made with the south direction i'm a bit confused with what u are referring to..

The bit you have marked in red should be $204 - 180 = 24$.

PS and although you don't necessarily need an accurate diagram, your velocity is at a bearing of approximately 225 degrees. If you had drawn it more accurately, you would see that can't be 66 degrees.

 

[kuruman]

OHH wait is the angle 66 degrees meant to be between the sunlight line and the vector 0.36.. sorry about that!! for the angle made with the south direction i'm a bit confused with what u are referring to..

As your drawing shows, the angle between the Sun's rays and the fly's velocity is 66°. The question is which trig function, sine or cosine, goes with the velocity component along the wall and why. This question was raised by @PeroK in post #4. "The angle made with the south direction" is the 24° angle formed between the fly's velocity vector and the down arrow representing the southerly direction.

Note that these angles are complementary, i.e. sin(24°) = cos(66°) and cos(24°) = sin(66°).

 

[jbriggs444]

Homework Statement: A fly in a room is flying on a bearing of 204

I suspect that the intended meaning mean that the fly is flying on a heading of 204 in still air.

"Bearing" is the direction from a reference point to a particular object. e.g. Which way from the fly to the sun?

"Heading" is the aiming direction of a moving object. e.g. Which direction is the fly's head pointing?

"Course" is the direction the object is actually moving. This can vary from heading if there is wind, current or side slip.

 

[kuruman]

"Bearing" is the direction from a reference point to a particular object. e.g. Which way from the fly to the sun?

I wasn't sure about the meaning of bearing myself. This is what I got when I googled, "What is a bearing of 204?"

It didn't seem to be relevant to the question, so I googled, "What is a bearing of 204 degrees?" and I got this

Units are important !

 

[jbriggs444]

I wasn't sure about the meaning of bearing myself. This is what I got when I googled, "What is a bearing of 204?"

It didn't seem to be relevant to the question, so I googled, "What is a bearing of 204 degrees?" and I got this
View attachment 366152

Yes, that passage is apt. An absolute bearing (or heading or course) would typically use a 360 degree rosette as described above with 0 to the north, 90 to the east, 180 to the south and 270 to the west.

One can also use relative directions. e.g.

"Where does she bear?"
"Two points off the port bow" (four points being 45 degrees).

or

"Bandits at 11 o'clock high".

Regardless of the scale being used, a "bearing" is the direction to an object, a "heading" is the direction a craft is facing and a "course" is the direction of a vessel's resulting path.