Hit or miss?
You are standing in the midst of the Sahara Desert, at the coordinates .
From there, you launch a projectile aiming exactly North, at Greenwich . Where will the projectile land?
A.
In the
Western Hemisphere
B.
In the
Eastern Hemisphere
C.
On the
Greenwich Prime Meridian
Details and Assumptions
- Don't forget to take Earth's rotation into consideration.
- Assume Earth to be a uniform solid sphere.
- Ignore effects of air resistance and wind.
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1 solution
We can solve this problem in two different frames of reference: in an inertial frame and in Earth's frame.
Frame 1: Inertial frame of reference
When we observe the situation from an inertial frame, we see that the Earth is rotating. Points that closer to the equator move in a bigger circle, and therefore faster, as compared to points near the poles. This means that the Sahara desert has a greater tangential velocity than Greenwich. When the projectile is launched from the desert, it carries that greater tangential velocity, and is moving east faster as compared to Greenwich. Therefore, by the time the projectile reaches the same latitude as Greenwich, it has moved more eastwards than Greenwich. Thus, it lands east of Greenwich, in the eastern hemisphere.
Frame 2: Earth's frame of reference
Note that this is a non-inertial frame. The projectile will appear to have non-zero velocity towards east, even though it was launched exactly north. This phenomenon can be explained using the coriolis force , which is a fictitious force . Fictitious forces are usually required to explain equations of motion in non-inertial frames of reference.