A canoe has a velocity of 0.48 m/s southeast relative to the earth. The canoe is

Question

A canoe has a velocity of 0.48 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.48 m/s east relative to the earth. Part A Find the magnitude of the velocity of the canoe relative to the river. Express your answer using two significant figures. v = m/s SubmitMy AnswersGive Up Incorrect; Try Again; 11 attempts remaining Part B Find the direction of the velocity of the canoe relative to the river. Express your answer as an angle measured south of west. Express your answer using two significant figures. = south of west SubmitMy AnswersGive Up

Explanation / Answer

south east angle is 315°

finding the components (x and y) of the canoe’s velocity with respect to the river.

v(canoe, river) = v(canoe, earth) - v(river, earth)

So find the velocity for the x and y components.

angle for the canoe vs the earth is 315 ° (south east), but since the river is flowing directly east, the angle for the river vs the earth is 180 °.

vx(canoe, river) = vx(canoe, earth) – vx(river, earth)

vx(canoe, river) = 0.48*cos(315) + 0.48*cos(180)

vx(canoe, river) = -0.141

Now find the y component of the velocity:

vy(canoe, river) = vx(canoe, earth) – vx(river, earth)

vy(canoe, river) = 0.48*sin(315) + 0.48*sin(180)

vy(canoe, river) = -0.339

Now find the velocity by using the Pythagorean theorem:

v = sqrt(x^2 + y^2)

v = sqrt(-0.141^2 + -0.339^2)

v = 0.3675 m/s

b)

= atan(y / x)

= atan(-0.339 / -0.141)

= 67.42°

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