Professional Guidance for Kayaker in Tidal Current
What direction should the kayaker paddle in to travel straight across the harbor?
(a) In which direction should he paddle in order to travel straight across the harbor?
How long will it take the kayaker to cross the harbor?
(b) How long will it take him to cross?
Answer:
The kayaker should paddle at an angle of 36 degrees west of north to travel straight across the harbor. It will take him 31 seconds to cross the harbor.
Explanation:
Let the direction in which he pedals make an angle of θ with north across.
Sinθ = 2 / 3.4
θ = 36 degrees (west of north)
b) Component of his velocity along the north = 3.4 cos 36
= 2.75 m/s
Time required = 85 / 2.75 s
= 31 seconds
For a kayaker navigating a tidal current, understanding the direction and speed of the current is crucial for efficient paddling. In this scenario, the kayaker needs to paddle north across an 85m wide harbor with a tidal current flowing to the east at 2.0 m/s.
By calculating the angle at which the kayaker should paddle, which is 36 degrees west of north, the kayaker can travel straight across the harbor. This optimal angle allows the kayaker to counteract the effects of the eastward flowing current and reach the opposite side efficiently.
Furthermore, to determine the time it takes to cross the harbor, the kayaker's velocity component along the north direction is calculated to be 2.75 m/s. Dividing the width of the harbor by this velocity component yields a crossing time of 31 seconds.
By following these calculations and recommendations, the kayaker can navigate the tidal current effectively and reach the other side of the harbor in a timely manner.