Q15. As shown in the image below, a man starts from point A, and tries to swim across a 40-ft wide river to point B on the other side, downstream at a distance d. The river flows with a constant velocity v₁ = 2.1 ft/s, with direction shown in the image. The man can swim at a speed Vm/r = 5.2 ft/s in still water (which is the relative constant speed with respective to the flowing water). If the distance d = 52 ft, determine the magnitude of the man's absolute speed vm (with the effect of the flowing water) so he can arrive at point B. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. Vr 40 ft d B d Vm/r Vr Ez 40 ft V m B
Q15. As shown in the image below, a man starts from point A, and tries to swim across a 40-ft wide river to point B on the other side, downstream at a distance d. The river flows with a constant velocity v₁ = 2.1 ft/s, with direction shown in the image. The man can swim at a speed Vm/r = 5.2 ft/s in still water (which is the relative constant speed with respective to the flowing water). If the distance d = 52 ft, determine the magnitude of the man's absolute speed vm (with the effect of the flowing water) so he can arrive at point B. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. Vr 40 ft d B d Vm/r Vr Ez 40 ft V m B
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Step 1
Given that,
width of the river is
The distance from the other end to the point where the man reached on the other side is
The constant velocity of the river is
The velocity of a swimmer with respect to the river is
Assuming the vertical axis (from the starting point to the other ends) is y and the horizontal (towards the downflow) is the x-axis,
Let the swimmer makes an angle from the vertical towards the downstream. and the actual velocity of the swimmer makes an angle from the vertical
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