Consider a swimmer who wants to swim directly across a river as shown in the figure below. If the speed of the current is 0.29 m/s and the swimmer's speed relative to the water is 0.64 m/s, how long will it take her to cross a river that is 14 m wide?
draw the velocity diagram. I assume the figure has him swimming slightly upstream and the current is keeping him in a straight across path.
His velocity upstream/relative water+ velocity of water=his resultant velocity
But these are vectors, and it is a right trianagle.
.64^2=hisvelocity^2 + current^2
hisvelocity^2=.64^2-.29^2
his velocity across= sqrt .3225 check that.
his velocity=.571 m/s
time across= distance/velocityabove
= 14/.572=24.5 seconds
check the math.
To find the time it will take for the swimmer to cross the river, we can break down the swimmer's motion into two components: one in the direction of the river's flow (downstream) and one perpendicular to the river's flow (across the river).
Let's first calculate the downstream velocity. Since the swimmer's speed relative to the water is 0.64 m/s and the current is flowing at 0.29 m/s, the swimmer's downstream velocity can be calculated by adding the two velocities together:
Downstream velocity = swimmer's velocity + current velocity = 0.64 m/s + 0.29 m/s = 0.93 m/s
Next, let's calculate the time it will take for the swimmer to cross the river, assuming she is swimming directly perpendicular to the river's flow. We can use the formula:
Time = Distance / Velocity
In this case, the distance is the width of the river, which is given as 14 m, and the velocity is the downstream velocity calculated earlier, which is 0.93 m/s:
Time = 14 m / 0.93 m/s ≈ 15.05 seconds
Therefore, it will take approximately 15.05 seconds for the swimmer to cross the river.