Question

Two canoeists start paddling at the same time and head toward a small island in a lake, as shown in the figure (Figure 1). Canoeist 1 paddles with a speed of 1.55 m/s at an angle of 45 ∘ north of east. Canoeist 2 starts on the opposite shore of the lake, a distance of 1.5 km due east of canoeist 1.

a. In what direction relative to north must canoeist 2 paddle to reach the island?

b. What speed must canoeist 2 have if the two canoes are to arrive at the island at the same time?

Answer 1

the left hand triangle is isosceles (45-45-90)

so the base is also 1.0 km

leaving 1.5-1.0 = 0.5 km as the base of the right hand triangle

d1 = 1.0 / sin45 = 1.414 km

d2^2 = 1.0^2 + 0.5^2 = 1.25

d2 = 1.118 km

to get there at the same time

their speeds will be directly proportional to the distances

v2/v1 = d2/d1

v2/1.55 = 1.118 / 1.414

v2 = 1.226 m/s (answer b)

the vertex angle of right hand triangle is the same as theta in the diagram (alternate interior angles)

tan(theta) = 0.5 / 1.0 = 0.5

theta = 26.6° (answer a)