So many models fail at basic reasoning.
> What weighs more: a pound of feathers or a great british pound?
> A pound of feathers and a Great British Pound weigh the same, which is one pound.
It works if you add "Think step by step," though.
> What weighs more: a pound of feathers or a great british pound?
> A pound of feathers and a Great British Pound weigh the same, which is one pound.
It works if you add "Think step by step," though.
Derivations of well known problems trip these models up big time.
Which bullet lands first, a bullet shot horizontally or one shot towards the ground
The bullet shot horizontally will land first, assuming both bullets are fired from the same height and with the same initial velocity. This is because the bullet shot horizontally has a horizontal velocity component that causes it to travel forward while it falls under gravity. The bullet shot towards the ground only has the force of gravity acting on it, causing it to accelerate downwards. Therefore, the bullet shot horizontally will hit the ground later than the one shot towards the ground
Even if you ask it to think step by step, it gets confused:
Bullet shot towards the ground: When a bullet is shot towards the ground, it has both an initial horizontal and vertical velocity components. However, since we're only interested in comparing the time it takes for each bullet to reach the ground, we can focus on their vertical velocities and ignore their horizontal velocities.
Let's denote:
( v_y ) as the initial vertical velocity of the second bullet (which is zero in this case) Using the same equation of motion in the vertical direction: [ y = h - \frac{1}{2}g(t')^2 ] Since ( v_y = 0 ), we have: [ t' = \sqrt{\frac{2h}{g}} ](Edit: I initially thought Gemini got it wrong but I read the answer again and it's actually right!)