B The horizontal speed of an object does not affect the time it takes to fall vertically?

[user079622]

He didnt plug horizontal speed in any equation, which implies it is irrelevant for this problem.

My intuition say that if I throw a bullet from 1.5m height, with horizontal speed of 10m/s it will take less time to hit the ground, than if I shot this bullet from gun at 1000km/h in horizontal direction.

Why my intuition fail, why I am wrong?

 

[PeroK]

Why my intuition fail, why I am wrong?

The universe doesn't care about human intuition.

 

[user079622]

The universe doesn't care about human intuition.

Without put problem on paper, you will say that time duration is equal?

 

[berkeman]

Without put problem on paper, you will say that time duration is equal?

Yes, I can say it is true from my experience with shooting and ballistics. When we calculate the drop of a bullet fired horizontally, we take the horizontal flight time from the gun to the target, and use that time to tell us the vertical drop.*

* (ignoring air resistance slowing the horizontal motion of the bullet, which does need to be taken into account for longer shots in order to get a better approximation of the horizontal velocity)

 

[PeroK]

Without put problem on paper, you will say that time duration is equal?

Yes. Unless the speed is sufficient for the curvature of the Earth to become relevant.

That said, there is also aerodynamics to take into account.

 

[A.T.]

Why my intuition fail, why I am wrong?

Because your intuition is trained on real world situations (where many factors are at play), not idealized scenarios (which are meant to demonstrate one aspect in isolation, and are supposed to be easy to solve).

For a frisbee, the horizontal velocity obviously matters for the time it stays airborne, because of its aerodynamics, which is often neglected in idealized problems.

 

[kuruman]

Why my intuition fail, why I am wrong?

Watch this video of a classic demonstration. Is what you see consistent with your intuition?

 

[PeroK]

Because your intuition is trained on real world situations (where many factors are at play), not idealized scenarios (which are meant to demonstrate one aspect in isolation, and are supposed to be easy to solve).

For a frisbee, the horizontal velocity obviously matters for the time it stays airborne, because of its aerodynamics, which is often neglected in idealized problems.

This is the reason that the underlying laws of nature went undiscovered for so long. Newton saw what no one else had previously seen: that hidden beneath the variety and complexity of motion lay four laws - the three laws of motion and the law of gravitation.

Birds and aeroplanes apparently defy the law of gravity!

 

[user079622]

Watch this video of a classic demonstration. Is what you see consistent with your intuition?

Yes, I know if I jump in train, I will land at same place if train travel at constant speed.

 

[user079622]

This is the reason that the underlying laws of nature went undiscovered for so long. Newton saw what no one else had previously seen: that hidden beneath the variety and complexity of motion lay four laws - the three laws of motion and the law of gravitation.

Do you think his discover of calculus is even bigger then laws of motion?

 

[kuruman]

Yes, I know if I jump in train, I will land at same place if train travel at constant speed.

What if the train is not moving at constant speed, but it accelerating? Watch this especially the last part when the acceleration is provided by tilting the track away from horizontal. The result will be the same whether the cart is released from rest down the incline or given a push up the incline.

 

[user079622]

What if the train is not moving at constant speed, but it accelerating? Watch this especially the last part when the acceleration is provided by tilting the track away from horizontal. The result will be the same whether the cart is released from rest down the incline or given a push up the incline.

Ball is fired at angle in last part. Oblique shot

 

[kuruman]

Ball is fired at angle in last part. Oblique shot

An angle with respect to what? "Oblique shot" does not explain much.

 

[user079622]

An angle with respect to what? "Oblique shot" does not explain much.

Respect to horizontal

 

[user079622]

An angle with respect to what? "Oblique shot" does not explain much.

If ball is fired vertically, it will fall behind truck.

 

[jbriggs444]

If ball is fired vertically, it will fall behind truck.

Vertically according to whom?

If vertical with respect to the rest frame of the ground then yes, the truck will move away forward before the ball falls.

If vertical with respect to the truck then, to a first approximation, it will fall back into the truck. To a better approximation, Coriolis will do its thing.

 

[kuruman]

Assume that the cart is moving down the incline with speed $u$ when the ball is fired with speed $v$ in a direction perpendicular to the incline. The angle of the incline is $\theta$. Can you show with equations, not intuition, that the ball will fall back into the cart regardless of the values of $u$, $v$ and $\theta$? Ignore the Coriolis effect mentioned in the previous post.

 

[Lnewqban]

He didnt plug horizontal speed in any equation, which implies it is irrelevant for this problem.

The only forces affecting the time an object takes to fall vertically are vertical forces.
Think of forces induced by wings and parachutes, which retard a fall.
Examples of increased fall speeds:
-Peregrine falcons can reach vertical speeds of up to 200 mph when diving.
-Thrust from the engine allows special aircraft reach vertical speeds greater than free fall (dive bombers, aerobatic planes).
-The free end of a board that rotates about a pivot under the force of gravity will accelerate at a rate greater than g.

 

[user079622]

Vertically according to whom?

If vertical with respect to the rest frame of the ground then yes, the truck will move away forward before the ball falls.

If vertical with respect to the truck then, to a first approximation, it will fall back into the truck. To a better approximation, Coriolis will do its thing.

Vertically respect to ground, parallel with gravity direction.

Assume that the cart is moving down the incline with speed $u$ when the ball is fired with speed $v$ in a direction perpendicular to the incline. The angle of the incline is $\theta$. Can you show with equations, not intuition, that the ball will fall back into the cart regardless of the values of $u$, $v$ and $\theta$? Ignore the Coriolis effect mentioned in the previous post.

No without help of textbook.

 

[kuruman]

No without help of textbook.

OK, this is not a class exam. Consult with your textbook and once you get your solution post it here. There are more than one ways to get the answer.

 

[A.T.]

Vertically respect to ground, parallel with gravity direction.

It's not about what 'vertical' means. It's about which reference frame measures the velocity to be vertical. Gravity has the same direction in all frames, but velocity vectors are frame dependent.

 

[ketoenol]

Mythbusters did this exact demonstration in Season 7, Episode 12. Just because something is non-intuitive doesn't mean that it's not true!

 

[jackjack2025]

He didnt plug horizontal speed in any equation, which implies it is irrelevant for this problem.

My intuition say that if I throw a bullet from 1.5m height, with horizontal speed of 10m/s it will take less time to hit the ground, than if I shot this bullet from gun at 1000km/h in horizontal direction.

Why my intuition fail, why I am wrong?

Maybe because your intuition is unconsciously assessing distance travelled to time.