a person throws a stone vertically upward while sitting in a bus moving with constant velocily :) where the stone will fall -

a )in his hand
b )behind him
C )in front of him
d )beside him
And why

While the stone is in the air, it retains the same horizontal velocity component as the bus. In a bus-fixed coordinate system, the stone goes straight up and down, landing in his hand.

The stone will fall behind him, because you are in horizontal motion and the stone is in vertical motion, so the stone will fall slightly behind you due to the horizontal velocity which is higher than the vertical velocity.

To determine where the stone thrown vertically upward will fall, we need to consider the different velocities at play here. Let's break it down step by step:

1. The person throws the stone vertically upward while sitting in a moving bus.
2. Since the stone is thrown vertically upward, its initial velocity is positive (upward) relative to the person's hand.
3. The bus is moving with a constant velocity.
4. Combining the velocities of the person and the bus gives the overall velocity of the stone.

Now, let's analyze the options one by one:

a) In his hand: If the stone falls back into the person's hand, it implies that the stone's overall velocity, including the velocity of the bus, matches the velocity of the person's hand. This scenario is very unlikely because the stone is thrown upward, which means it should have a different velocity from the person's hand. Therefore, option a is not the correct answer.

b) Behind him: If the stone falls behind him, it implies that the overall velocity of the stone, including the velocity of the bus, is greater in magnitude than the velocity of the person's hand. Since the stone is thrown vertically upward, it would continue its upward motion but with a gradually decreasing velocity due to the opposing force of gravity. Thus, the stone will not fall behind the person. Therefore, option b is not the correct answer.

c) In front of him: If the stone falls in front of him, it implies that the overall velocity of the stone, including the velocity of the bus, is smaller in magnitude than the velocity of the person's hand. As mentioned earlier, the stone is thrown upward, so it will eventually reach its highest point and then start to fall back down. If the velocity of the stone is smaller than the person's hand, it means it is not able to catch up with the moving bus. Therefore, the stone will fall in front of the person. Therefore, option c is the correct answer.

d) Beside him: This option is highly unlikely because the stone is thrown vertically upward, not horizontally. The direction of the stone's motion is mostly determined by the vertical component, affected by gravity. As a result, it is improbable for the stone to fall beside the person. Therefore, option d is not the correct answer.

In conclusion, the stone will fall in front of the person (option c) because the stone's overall velocity, considering the velocity of the bus, is smaller in magnitude than the person's hand's velocity.