Important Kinematics Physics

Question

a-  A particle is projected vertically upwards with initial speed u m.s^-1 , after T s it reaches its greatest height , H m .

Find , in terms of u and g, an expression for :

 

i - T                 ii - H

 

b- At a certain time the particle is travelling upwards through a point A,at a height of 19.6 m, and 2 s later it is at a point B, at a height of 29.4 m .

 

i- show that it is on its way down through B at that time .

 

ii- Find the value of u .

Answer 1

Hi Nona!

 

Question a is asking you to solve for kinematic quantities associated with reaching maximum height.  It wants you to solve (in terms of given quantities and constants) for the time and the maximum height (displacement).  To do that, you must know the three other kinematic quantities for this situation:

 

initial velocity

acceleration

final velocity

 

The question to ask is, do you know those three quantities for this vertical motion, either by having them be given or having them defined by the situation?  I think you do, but take a look at it and see if you can figure out how.

 

Then, you take those known values and, to calculate t, use the kinematic equation that involves initial velocity, final velocity, acceleration, and time.  To solve for the height, use the equation that involves those three quantities and displacement.

 

See if you can work that one out, and let me know if you want to look at it further.

 

For Question B, the key is how to show that the particle is on its way down.  You should note that the sign of velocity always indicates the direction of motion.  So, as the second part of B would suggest, you should try solving for the final velocity of this motion.

 

As usual, you will have to know three other quantities from among initial velocity, displacement, acceleration, and time, for the motion described.  I think you have information and knowledge that will tell you what three of those quantities are for this case, but see if you can figure out how.  This should let you determine the magnitude of the final velocity, as well as its sign (which indicates direction).

 

I hope this gets you started.  Just let me know if you want to talk about this in more detail.