Can someone please help me sort out this problem? "A boy standing at the equator jumps vertically into the air. Does he land in the exact same spot after landing?" I'm thinking that when he jumps he is also moving horizontally with the earth and so he will land in the same spot. But, I'm not sure how to explain it properly in terms of physics. Does it have to do with inertial frame of reference?
The boy's motion relative to EArth is vertical, and Gravity pulls him back to the initial position.
Thanks!
To understand if the boy will land in the exact same spot after jumping vertically, we need to consider a few principles of physics.
First, let's talk about the rotational motion of the Earth. The Earth rotates around its axis, completing one full rotation approximately every 24 hours. As a result of this rotation, objects on the Earth's surface, including the boy, are moving at the same angular velocity as the Earth itself.
When the boy jumps vertically, he acquires some vertical velocity. However, the crucial point is that the horizontal velocity he had before jumping is not lost. According to the law of conservation of angular momentum, an object on the surface of the Earth will continue to move with the same angular velocity unless acted upon by an external force.
Therefore, since the boy retains his original horizontal velocity while jumping, and the Earth keeps rotating at the same angular velocity, he will indeed land in nearly the same spot after jumping. This is irrespective of the fact that the Earth is moving horizontally.
To summarize, the concept of an inertial frame of reference in physics helps explain why the boy lands in the same spot. An inertial frame of reference is a frame where Newton's first law of motion holds. In this case, we can consider an inertial frame of reference attached to the Earth's surface, where the horizontal motion of the boy is unaffected by the Earth's rotation.
It's important to note that while in theory, the boy should land in the same spot if we only consider the Earth's rotation, other factors like air resistance, the movement of the Earth around the Sun, and geological variations can cause slight deviations from an exact landing spot. Nonetheless, on a small scale, the effect of these factors is minimal.