Answer:
The teacher should swim in a direction 29.24° North of East
Explanation:
Given that the there is a water current across the lake, and the physics teacher intends to swim directly across the lake, the direction the physics teacher will have to swim is found as follows;
The speed of the water current is given by the speed of the floating leaf traveling with the water current
Distance traveled by the leaf = 4.2 m South
Time of travel of the leaf = 5.0 s
Speed of leaf = 4.2/5 = 0.84 m/s = Speed of the water current
Swimming peed of the teacher, v = 1.9 m/s
To swim directly across the lake, the teacher has to swim slightly in the opposite direction of the water current, the y-component of the teacher's swimming speed should be equal to and opposite that of the speed of the water current.
Y-component of v = v×sin(θ), where θ is the angle of the direction, the teacher should swim
Therefore;
1.9 × sin(θ) = 0.84
sin(θ) = 0.84/1.9 = 0.44
θ = 26.24°
That is the teacher should swim in a direction 29.24° North of East.