Student Resources
Related Rates: Spotlight
Bob is running away from his study group along the front of Edmon Low Library. But Cara has set up a spotlight 15 meters from the corner of the building and is keeping it pointed at Bob while the other members of the study group chase him down.
If Bob is running at a constant speed along the wall and away from the nearest corner to Cara, describe, in general terms, how Cara must turn her spotlight to keep Bob lit up.
Let \(x\) represent Bob's distance along the wall, in meters, from the corner nearest to Cara (shown measured along the horizontal line in the diagram above). As shown in the diagram, let \(\theta\) be the angle, in radians, at which Cara must point her spotlight to keep Bob illuminated. Write an equation relating \(x\) and \(\theta\). It does not need to be solved for any particular variable.
Let \(x\) represent Bob's distance along the wall, in meters, from the corner nearest to Cara (shown measured along the horizontal line in the diagram above). As shown in the diagram, let \(\theta\) be the angle, in radians, at which Cara must point her spotlight to keep Bob illuminated. Find an equation that relates \(\displaystyle\frac{dx}{dt}\) and \(\displaystyle\frac{d\theta}{dt}\).