You are on a boat in the middle of the Pacific Ocean at the equator traveling in a hydrofoil
going at a constant speed of 300 /. The water is perfectly still. What is your acceleration:
a) If you’re heading due North?
b) If you’re heading due East?
c) If you’re heading straight up (something probably went wrong at this point).
You may assume the following:
The earth has a radius of 6371 km.
The earth makes one full revolution every 24 hours.
The gravitational constant at sea level is 9.81 m/s2
East and North are relative to the Earth’s axial north, not magnetic north.

a)If the boat is going along North from equator, there will be only centrifugal force acting along upward direction which will be balanced by the weight of boat.

Angular velocity ω= (2π / (3600 x 24)) = 7.27 x 10⁻⁵ rad/s

Acceleration due to centrifugal force a = 0.0337m/s²

Centrifugal force due to its own velocity 300 m/s is v²/r = 0.0141 m/s².

Total acceleration will be 0.0141 +0.0337 =0.0478m/s².

Thus, if you’re heading due North, total acceleration will be 0.0478 m/s².

b) If the boat goes along East, Coriolis acceleration is in the direction of centrifugal force.

Coriolis acceleration is (2 x 7.27 x 10⁻⁵ x300 ) = 0.0436m/s².

Total centrifugal acceleration due to centrifugal force = 300 + (7.27 x 10⁻⁵ x 6371 x 10³) = 0.0436 m/s².

Total acceleration is 0.0436 + 0.0367 = 0.0803m/s².

Thus, if you’re heading due East, acceleration will be 0.0803 m/s².

c) When boat is going upward, centrifugal force will change with time. but Coriolis acceleration remains same.

Thus, if you’re heading straight up, no exact value for acceleration.

Learn more about acceleration.

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