Question 20.1: Sample Exercise: Rowing With and Against the Current Two row...
Sample Exercise: Rowing With and Against the Current
Two rowers, Derek and Teresa, are in a boat. Derek can row at a steady speed of 3.8 MPH, and Teresa can row at a steady speed of 4.6 MPH. If the water in the stream is moving at a speed, v_{we}, of 4.0 MPH relative to the bank, determine the velocity of the boat relative to the earth (or bank), v_{be}, when
a) Derek rows against the current,
For Derek, v_{bw}= 3.8 MPH
v_{bw}= 3.8 MPH
v_{we}= -4.0 MPH
v_{be}= ?
b) when Teresa rows against the current,
For Teresa, v_{bw}= 4.6 MPH
v_{bw}= 4.6 MPH
v_{we}= -4.0 MPH
v_{be}= ?
and c) when Derek rows with the current.
For Derek, v_{bw}= -3.8 MPH (downstream)
v_{bw}= -3.8 MPH
v_{we}= -4.0 MPH
v_{be}= ?
We will assume that the direction of the current, downstream, is negative. Therefore, if a velocity is positive the movement is upstream (or against the current), and if it is negative the movement is downstream (or with the
current).
a. v_{be}= v_{bw} + v_{we}
v_{be}= 3.8 + (-4.0)
v_{be}= -0.2 MPH (downstream)
b. v_{be}= v_{bw} + v_{we}
v_{be}= 4.6 + (-4.0)
v_{be}= +0.6 MPH (upstream)
c. v_{be}= v_{bw} + v_{we}
v_{be}= -3.8 + (-4.0)
v_{be}= -7.8 MPH (downstream)