Calculate the joggers average velocity

AI Thread Summary
To determine the canoeist's path across the river, he must head upstream at an angle to counteract the downstream current, requiring calculation of the y-component of his velocity. The trip duration can be calculated using the width of the river and the effective velocity across it. For the jogger, the displacement involves breaking down his two runs into x and y components, leading to a total displacement vector. The average velocity is then derived from this displacement over the total time taken. Accurate trigonometric calculations are essential for both scenarios to achieve the correct results.
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A canoeist wants to travel straight across a river that is 0.10 km wide. However, there is a strong current moving downstream with a velocity of 3.0km/h. The canoeist can maintain a velocity realitive to the water of 4.0km/h.
a) In what diretion should the canoeist head to arrive at a position on the other shore directly opposite to his starting position?
b) How Long will the trip take him?
AND
A jogger runs 15km(N 35 degrees E) and then runs 7.5 km (N 25 degrees W) It takes a total of 2.0 hours to run,
a)determine the displacement of the jogger
b)calculate the joggers average velocity
(I have to break this one into x and y components but I just can't seem to get it right).
 
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For the canoist, call x the axis across the river, and y the axis going parallel to the river. What must be the y component of the canoe? How can you then solve for the x component?

For b, what are the standard trig formulae for x and y components?
 
First one:
c²=a²+b²
4²=3²+b²
16-9=b²
b=2.65

Tan= opp/adj
tan=3/4
=o.75*tan-1
=37 degrees
answer is suppose to be 41

Second one:
x components:12.29+(-3.17)=9.12
y components=8.60+6.79=15.39
83.1744+236.8521=c²
320.0265=c²
c=18

answer is suppose to be 2.0*10¹ km(N 16 degrees east)
 
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