don't we consider the mass( calculus question)?

Question

the problem: a stone is thrown with an initial speed of 10 m/s. How high it will rise?
Solution: acceleration is a=-g so
v(t) = -gt+10, x(t)=-gt^2/2+10t, you equate v with 0, find t and replace for x....
My question: don't we consoder the mass since, if you throw a light stone will go furhter than a heavy one?

Answer 1

This is more of a physics question.
A light stone won't go farther than a heavy one. If the initial speed is the same and you are neglecting air resistance, the only acceleration acting on the stone is gravity. This is just like if you drop a piece of paper and a brick in a vacuum. They will both accelerate at the same rate, about 9.81 m/s^2. The only reason the paper falls slower in real life is the force of air resistance.

Answer 2

When you throw the speed like that, the only way you interact with the stone is by giving it a constant upward speed -you do not exert any force while it is moving. So the only force applying on the stone is its weight, facing downwards:
The math part:
mg=ma=Total force
|a|=g=constant so you move to the equations you know.(acceleration is the derivative of speed, so you integrate to get speed /you apply the equation v=vinitial + acceler.x time etc).
Indeed, if you throw a light stone, it can go further than a heavy one, but the result depends on the initial speed you give (to give this initial speed you apply some force. If you apply the same force to two different masses, they will just rise with different initial speeds (or so I believe. Think of these instead: which stone is easier to lift: a pebble or a rock? Just because you have the impression that something is easier to lift when it is light, it doesn't mean that it will move further. What did Galileo prove?)
And yes, it has to do a lot with physics.

Answer 3

The mass matters when you are given the initial force acted on the object and asked to determine velocity from that. Gravity acts on all objects equally, doesnt matter the mass. If you throw 2 stones of different masses and start them with the same velocity they would go the same distance ( this assumes no air resistance). However if you use the same Force to throw those same two stones they will travel different distances.

Answer 4

The only force acting on the stone is that of gravity acting vertcally downward (if we neglect air-resistance): there is no horizontal force.

The Vx = Vocosz where z is the angle at which the stone is launched. Similarly, Vy = Vo sinz

The position of the stone at any time t is given by
x = (Vo cos z)t , y = -.5gt^2 + (Vo sin z)t

If you eliminate t from the above two parametric equations, you get: y = -g/(2Vo^2cos^2 z) +x tan z which is a parabola with vertical axis of symmetry.

Answer 5

That's taken into account as part of the initial speed/velocity.

OR

If you drop a heavy rock and a light rock [of the same size] from the same height at the same instant, which will strike the ground first?