uberathlete
New member
- Joined
- Jan 16, 2006
- Messages
- 48
Hi again everyone. I have a solution to this problem but I'm not really sure if it's correct. The problem is:
The position of a fly at time t is given (x, y, z) = (t, t^2, 1+t^2). A light shines down on the fly from the point (0, 0, 3) and casts a shadow on the xy-plane. What is the position and velocity of the shadow at time t = 1?
What I have is:
The position of the fly at t is (x,y,z) = (t, t^2, 1+t^3). The shadow is on the xy-plane, so it's position is (x,y,z) = (t, t^2, 0). Therefore it's velocity is v(t) = (1, 2t, 0). So at time t = 1, the position of the shadow is: (x, y z) = (1, 1, 0) and its velocity is v(t) = (1, 2, 0).
Now I'm not really sure if this is correct, cuz the light source is at (0, 0, 3) while the fly at time t=1 is at (1, 1, 2), so essentially, the light is casting a diagonal light on the fly which may affect the position of the shadow. I'm not really sure how to go about this, so if anyone could lend me a hand or a thought, it'd be greatly appreciated. Thanks!
The position of a fly at time t is given (x, y, z) = (t, t^2, 1+t^2). A light shines down on the fly from the point (0, 0, 3) and casts a shadow on the xy-plane. What is the position and velocity of the shadow at time t = 1?
What I have is:
The position of the fly at t is (x,y,z) = (t, t^2, 1+t^3). The shadow is on the xy-plane, so it's position is (x,y,z) = (t, t^2, 0). Therefore it's velocity is v(t) = (1, 2t, 0). So at time t = 1, the position of the shadow is: (x, y z) = (1, 1, 0) and its velocity is v(t) = (1, 2, 0).
Now I'm not really sure if this is correct, cuz the light source is at (0, 0, 3) while the fly at time t=1 is at (1, 1, 2), so essentially, the light is casting a diagonal light on the fly which may affect the position of the shadow. I'm not really sure how to go about this, so if anyone could lend me a hand or a thought, it'd be greatly appreciated. Thanks!