Rock thrown off a horizontal cliff

[Kiana Hill]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

The question states a stone is thrown off a cliff horizontal and it eventually hits the ground. A second stone is dropped from rest at the same height and it hits the ground too. The question asks which are the following quantities are the same or different; displacement, speed right before it hits the ground and time. I know that displacement for the first stone is greater because the resultant is greater. The time, I know, is the same but I believe it is because the initial height is the same so it would take the same amount of time. What I don't get is the speed right before it hits the ground. I am guessing it has to do with the component of velocity, vx and vy but I'm not sure why. All I know for sure is for the first stone, the velocity is the same as the vy and there is no vx, and for the second stone the velocity is at an angle right before it hits the ground but why does that necessarily mean, the velocity is greater?

 

[lewando]

Exaggerate the situation--imagine a bullet dropped from your hand and another bullet fired horizontally from a gun. Which will have the greater speed (magnitude of resultant velocity vector) upon impact?

 

[Kiana Hill]

Exaggerate the situation--imagine a bullet dropped from your hand and another bullet fired horizontally from a gun. Which will have the greater speed (magnitude of resultant velocity vector) upon impact?

That makes way more senses.

 

[haruspex]

why does that necessarily mean, the velocity is greater?

Same reason as for displacement: v_y is the same for both but v_x is different.

 

[bland]

I'm assuming that this is one of those weightless strings and frictionless planes type of thought experiment. Therefore my first thought was that the vertical component of velocity will be the same as they will both have been falling for the same time prior to hitting the ground, but one has had extra energy imparted to it in the form of momentum therefore the speed that generates must be in addition to the vertical velocity.