Can you solve this problem using this equation Vac = Vab + Vbc Which I think can

Question

Can you solve this problem using this equation

Vac = Vab + Vbc

Which I think can be rewritten as

Vab = Vac + Vcb

(Figure 1) A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance di (from A to C) is 200 m, the distance d2 (from C to B) is 150 m, and the speed r of the current in the river is 5 km/hour. Suppose that the swimmer's velocity relative to the water makes an angle of 45 degrees with the line from A to C, as indicated in the figure Part A To swim directly from A to B, what speed Us, relative to the water, should the swimmer have? Express the swimmer's speed numerically, to three significant figures, in kilometers per hour us= 4.04 km/hour Figure 1 of 1 Submit Hints My Answers Give Up Review Part dh Correct Another way to do this problem is to add the swimmer's and the river's velocities vectorially and set the angle that the resultant vector makes with AC or the river bank equal to that which AB makes with the same Provide Feedback Continue v, = 5 km/hour

Explanation / Answer

velocity of swimmer with respect to water,
vsw = -us * sin 45 x + us*cos 45 y
= - 0.707 us x + 0.707 us y km/hr

velocity of water with respect to ground,
vwg = 5 xkm/hr

vsg = vsw + vwg
= ( - 0.707 us + 5) x + 0.707 us y

d2 = vsgx *t
d2 = ( - 0.707 us + 5) *t ...eqn 1

d1= vsgy*t
d1 = 0.707 us * t ...eqn 2

divide eqn 1 by eqn 2
d2/d1 = ( - 0.707 us + 5) / (0.707 us)
150/200 = ( - 0.707 us + 5) / (0.707 us)
0.707us = -0.943*us + 6.67
us = 4.04 m/s
Answer: 4.04 m/s

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.