Question

A boat sails for 5 hours at 30 mph in a direction 164°56'. How far south has it sailed (to the nearest mile)?

Answer 1

To determine how far south the boat has sailed, we can calculate the component of its velocity directed south by multiplying the velocity (30 mph) by the sine of the angle 164°56'. The boat has sailed approximately 12.46 miles south.

Step-by-step explanation:

To find out how far south the boat has sailed, we need to calculate the component of its velocity that is directed south.

Since the boat is sailing in a direction 164°56', we can break down its velocity into its north and south components.

The south component of the boat's velocity is given by multiplying the velocity (30 mph) by the sine of the angle 164°56', which is approximately 0.4154.

Therefore, the boat has sailed approximately 12.46 miles south (30 mph x 0.4154 = 12.46 miles).

Answer 2

Total distance covered = 5 x 30 = 150 miles
Angle of travel with respect to south pole = 180 - 164°56' = 15°4'

Let the distance southwards covered be x, then
cos 15°4' = x/150
Thus, x = 150 cos 15°4' = 144.84

Therefore, the distance covered southwards = 145 miles to the nearest mile.