# A Numerical on motion in one dimension .

by sankalpmittal
Tags: dimension, motion, numerical
 P: 758 1. The problem statement, all variables and given/known data A boy throws a ball with v velocity upwards as well as downwards . What will be the displacement covered by the two balls if air friction and external force or viscosity is neglected ? 2. Relevant equations According to me the equations of motions are relevant here . 3. The attempt at a solution ummm I case : u=0 t= 1 sec to gain velocity v v= v then s(displacement) = 1/2t(v+u) = 1/2v II case : u2=0 t2= 1 sec to gain velocity v v= v then s2(displacement) = 1/2t(v-u) = 1/2v If time = t seconds then of course t=t2 So s=s2=1/2v
 Mentor P: 41,440 I don't quite understand what you're doing here. Does u stand for the initial velocity? How can it be zero if you're throwing things?
P: 758
 Quote by Doc Al I don't quite understand what you're doing here. Does u stand for the initial velocity? How can it be zero if you're throwing things?
You hold ball in your hand , so it is at rest . Then you throw , so it gains velocity v in 1 second . Yes u stand for initial velocity .

Mentor
P: 41,440
A Numerical on motion in one dimension .

 Quote by sankalpmittal You hold ball in your hand , so it is at rest . Then you throw , so it gains velocity v in 1 second . Yes u stand for initial velocity .
Are you trying to analyze the motion of the ball while it's in your hand or after you've throw it? Once you've thrown it and it leaves your hand, it's just a projectile.
P: 758
 Quote by Doc Al Are you trying to analyze the motion of the ball while it's in your hand or after you've throw it? Once you've thrown it and it leaves your hand, it's just a projectile.
No the ball is thrown upwards in one direction and it makes the angle of 90 degree , its not a projectile .
Mentor
P: 41,440
 Quote by sankalpmittal No the ball is thrown upwards in one direction and it makes the angle of 90 degree , its not a projectile .
Once it leaves your hand it is.
P: 758
 Quote by Doc Al Once it leaves your hand it is.
http://www.filefactory.com/file/cce8f02/n/untitled.bmp

Mentor
P: 41,440
 Quote by sankalpmittal Since ball is vertically thrown, it should not be called 'projectile'.
It doesn't matter how you throw it--up, down, sideways--as soon as it leaves your hand it is a projectile. (Even if it moves only vertically, it's still a projectile. A simple case, since you don't have any horizontal motion to worry about.)

(FYI: I cannot access that site from my office, but I'll look at it later.)
P: 758
 Quote by Doc Al It doesn't matter how you throw it--up, down, sideways--as soon as it leaves your hand it is a projectile. (Even if it moves only vertically, it's still a projectile. A simple case, since you don't have any horizontal motion to worry about.) (FYI: I cannot access that site from my office, but I'll look at it later.)
Ok , I searched on the net , you are correct . But what about the numerical :

A boy throws a ball with v velocity upwards and another ball with same velocity downwards . What will be the displacement covered by the two balls if air friction and external force or viscosity is neglected ?

What will be the answer ???

Mentor
P: 41,440
 Quote by sankalpmittal Ok , I searched on the net , you are correct . But what about the numerical : A boy throws a ball with v velocity upwards and another ball with same velocity downwards . What will be the displacement covered by the two balls if air friction and external force or viscosity is neglected ? What will be the answer ???
If you want the vertical position as a function of time, use the kinematic formula:
y = y0 + v0t - 1/2gt2

Where v0 is the initial velocity. In one case the initial velocity will be +v; in the other, -v. That's the only difference between the two cases.
P: 758
 Quote by Doc Al If you want the vertical position as a function of time, use the kinematic formula: y = y0 + v0t - 1/2gt2 Where v0 is the initial velocity. In one case the initial velocity will be +v; in the other, -v. That's the only difference between the two cases.
Ok so you mean then in one case velocity is + while in other its - .

This means displacement of both the balls will be different according to you , right ??
Mentor
P: 41,440
 Quote by sankalpmittal Ok so you mean then in one case velocity is + while in other its - .
Yes.
 This means displacement of both the balls will be different according to you , right ??
The position as a function of time will be different for each case. The ball thrown upward first has to reach the highest point, then return to the starting position. At that point, it's exactly the same as the other ball started out--it's velocity is v downward.
P: 758
 Quote by Doc Al Yes. The position as a function of time will be different for each case. The ball thrown upward first has to reach the highest point, then return to the starting position. At that point, it's exactly the same as the other ball started out--it's velocity is v downward.
Ist Case : Throwing upwards

u=v
v=0 (on reaching highest point)

s1 = ut - 1/2gt1^2

2nd Case : Throwing downwards

u=0
v=v

s2 = ut2+ 1/2gt2^2
= 1/2gt2^2

Therefore s1 is not equal to s2 right ??
(Displacements of two balls are different right ??)
Mentor
P: 41,440
 Quote by sankalpmittal Ist Case : Throwing upwards u=v v=0 (on reaching highest point)
The initial velocity is +v. Why mention the velocity at the highest point?

 s1 = ut - 1/2gt1^2
As per the formula I gave before:
y = vt - 1/2gt2

 2nd Case : Throwing downwards u=0 v=v
I don't understand this. The initial speed is -v, not zero.

 s2 = ut2+ 1/2gt2^2 = 1/2gt2^2
As per the formula I gave before:
y = -vt - 1/2gt2

 Therefore s1 is not equal to s2 right ?? (Displacements of two balls are different right ??)
As I stated before, yes.
P: 758
 Quote by Doc Al The initial velocity is +v. Why mention the velocity at the highest point? As per the formula I gave before: y = vt - 1/2gt2 I don't understand this. The initial speed is -v, not zero. As per the formula I gave before: y = -vt - 1/2gt2 As I stated before, yes.

OK .

 Related Discussions Advanced Physics Homework 4 Introductory Physics Homework 3 Introductory Physics Homework 4 Introductory Physics Homework 1 Introductory Physics Homework 2