SPEED

[TWFM]

Hi e1,
Please help a thicky.
If a man climbs high enough to raise his potential gravitational energy to 2.8 kJ,
his mass is 75kg
and gravity is 9.8 m s^-1 then how would you find out how high he had climbed?
and if he jumped, what speed would he be doing when he hit the deck?

Many thanks TW

 

[Unco]

Are you familiar with \(\displaystyle \L \Delta E_p = mg \Delta h\) and \(\displaystyle \L {v_f}^2 = {v_i}^2 + 2ad\) ?

 

[TWFM]

I know delta Eg=mg delta h is that the same?
If you could explain the second equation in word form Im sure I can crack it.
thanku for replying

 

[Unco]

You need to clarify what you have covered in class so that we can do this problem with methods you are familiar with.

The first question (yes the formula is the same) lends itself to beginning physics, whereas the second question lends itself to both beginning physics and beginning calculus.

In beginning calculus, we antidifferentiate a=9.8, with respect to t, to get v and d, and use the initial conditions v=0 and d=0 when t=0.

In both cases we assume the man is effectively falling from rest.

 

[TWFM]

I have only just picked up the basics of physics im affraid,
would this equation work for his speed v^2=2Ek/m?
How could you work out his speed at various points of desent?

I tried working out his speed at floor level after jumping from 3.8m
and then working out his speed if he jumped from 4.8m and took his speed after 1m of fall and he was going faster after 1m than he was after 3.8m of fall?
does that make sense because it is makin my head hurt thining about it.

thanku

 

[Unco]

I have only just picked up the basics of physics im affraid,
would this equation work for his speed v^2=2Ek/m?

Energy is conserved:
Ep at beginning = Ek at end

That equation of yours will indeed give his final velocity; well done.

 

[TWFM]

Thanku,
how could i break down his desent into 1m time checks?
sorry to be a pain

 

[Unco]

He begins 3.8m above the found. His Ep here is 2400, given by mgh.

He falls 1m, so his height is now 2.8m. Here, Ep = 75*9.8*2.8=2058J.

Ep lost = Ek gained

That is,
Ep at 3.8m - Ep at new height = Ek gained

So after falling 1m,
2400 - 2058 = Ek

And velocity at that instant is found by Ek = 1/2 * 75 * v^2.

 

[TWFM]

Yes thanku very much for your time and help.
Tim