How Does the Speed of a Shadow Change with Time and Distance?

[fubag]

A small source of light S is located at a distance L from a vertical wall. An opaque object with a height of h moves toward the wall with constant velocity v(->) of magnitude v. At time t=0 , the object is located at the source S.

Find an expression for v_s, the magnitude of the velocity v_s(->) of the top of the object's shadow, at time t.
Express the speed of the top of the object's shadow in terms of t, V, L, and h.



**Please help, I just need someone to guide me in how to start this problem. As such, it confuses me.


Thanks!

 

[mjsd]

a few hints to think about:
-- draw a nice diagram and label everything
-- use trig, similar triangles, and kinematics to relate your variables t, v, L(t), h, s(t), where s(t) is the height of shadow at time t, and L(t) is the distance between source and object at time t
-- once you know displacement as function of t, velocity/speed should be easy.

 

[fubag]

[img=http://img340.imageshack.us/img340/7161/20955ayi4.th.jpg]


Here is a picture.

 

[learningphysics]

[img=http://img340.imageshack.us/img340/7161/20955ayi4.th.jpg]


Here is a picture.

try to get the shadow's size using similar triangles.

 

[fubag]

if I relate the shadow to the height of the opaque, what value should I assign using similar triangles.?

 

[learningphysics]

if I relate the shadow to the height of the opaque, what value should I assign using similar triangles.?

you have the ratio of the height of the object to the height of the shadow... you also have the distance L... what is the corresponding side in the smaller triangle.

 

[fubag]

Could I simply assign a letter for the smaller distance like L-w or something?

 

[learningphysics]

Could I simply assign a letter for the smaller distance like L-w or something?

sure... but even better than that... you can write that distance in terms of v and t...

 

[fubag]

after attempting (looking at the problem) for almost 4 hours, I am still lost as to what I should do...

In attempting to relate L with the smaller distance I still cannot properly figure out how to relate it to velocity and time given only a constant velocity and no acceleration.

Need a different strategy and/or approach to this problem please.

Please help!

 

[learningphysics]

after attempting (looking at the problem) for almost 4 hours, I am still lost as to what I should do...

In attempting to relate L with the smaller distance I still cannot properly figure out how to relate it to velocity and time given only a constant velocity and no acceleration.

Need a different strategy and/or approach to this problem please.

Please help!

At a time t, what is the distance from the light source to the object? The question gave you the velocity v. You also know at time t=0, the distance from the light source is 0...

 

[fubag]

well to determine distance I am going to say distance = (velocity) / (time)

so Distance from the light source = (v/t)?

 

[learningphysics]

well to determine distance I am going to say distance = (velocity) / (time)

so Distance from the light source = (v/t)?

distance = v * t

 

[fubag]

haha sorry, was in a hurry.

ok now that I have this distance = v * t and the larger distance is L and now what should be my next step?

 

[learningphysics]

haha sorry, was in a hurry.

ok now that I have this distance = v * t and the larger distance is L and now what should be my next step?

What can you say about the ratios of sides of similar triangles?