Related rates , angles of depression: You are going down an elevator with glass walls

[heyitsarnold6969]

You are going down an elevator with glass walls. Looking out to the street, you spot the lead singer of your favorite band. You quickly take out your phone, open the camera app and zoom in to shoot some video. When you are still 55ft from the ground level, your elevator is going down at a speed of 5ft/s and the celebrity is about 40ft from the base of the building and moving directly away from he building at a speed of about 2 ft/s. With all this movement, you need to tilt your phone(changing the angle of depression) to keep shooting the video. Determine how fast you need to tilt your phone?

I've tried to use the fact that the angles are congruent, but im just soooo such at what exact formulas do i need to take the derivative of!! please help with steps! I'm so stumpped..

 

[Deleted member 4993]

You are going down an elevator with glass walls. Looking out to the street, you spot the lead singer of your favorite band. You quickly take out your phone, open the camera app and zoom in to shoot some video. When you are still 55ft from the ground level, your elevator is going down at a speed of 5ft/s and the celebrity is about 40ft from the base of the building and moving directly away from he building at a speed of about 2 ft/s. With all this movement, you need to tilt your phone(changing the angle of depression) to keep shooting the video. Determine how fast you need to tilt your phone?

I've tried to use the fact that the angles are congruent, but im just soooo such at what exact formulas do i need to take the derivative of!! please help with steps! I'm so stumpped..

Did you draw an approximate sketch of the situation?

You'll need to derive the function to be used in this situation (from the sketch).

 

[stapel]

You are going down an elevator with glass walls. Looking out to the street, you spot the lead singer of your favorite band. You quickly take out your phone, open the camera app and zoom in to shoot some video. When you are still 55ft from the ground level, your elevator is going down at a speed of 5ft/s and the celebrity is about 40ft from the base of the building and moving directly away from he building at a speed of about 2 ft/s. With all this movement, you need to tilt your phone(changing the angle of depression) to keep shooting the video. Determine how fast you need to tilt your phone?

I've tried to use the fact that the angles are congruent, but im just soooo such at what exact formulas do i need to take the derivative of!! please help with steps! I'm so stumpped..

The "exact formula" is something that you need to create on your own. This requirement will continue through the homework and into the upcoming test! So:

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck? For instance, you started by drawing the vertical line for the camera's height above ground level, the horizontal line for the ground, and the slanty line for the "line of sight" between the camera and the target. What shape is created by these lines? What formula(s) can you apply to this? You noted the values of the height h and the along-the-ground distance x; you noted the rates of change dh/dt and dx/dt. You picked a formula, differentiated with respect to time t, and... then what?

Please be complete. Thank you!