1. A spotlight on the ground shines on the wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
2. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock.
So far related rates problems have been pretty easy since we have been using geometric figures. I can't come up with an equation for either of these so I can solve for the change of rate. Can someone help me come up with the equations and show me how to do it in case I get something similar to these in the future?
Hello, FalconPUNCH!
You left out a measurement in #2.
. . I'll pick a convenient value . . .
2. A boat is pulled into a dock by a rope attached to the bow of the boat and
passing through a pulley on the dock that is 6 m higher than the bow of the boat.
If the rope is pulled in at a rate of 1 m/s,
how fast is the boat approaching the dock when it is 8 m from the dock?Code:* P * | R * | * | 6 * | * | B * * * * * * * x
The boat is at , the pulley is at
The length of the rope is: . . and .
From Pythagorus, we have: .
Differerentiate with respect to time: .
. . and we have: .
Can you finish it now?