Can anyone help me with this physics problem?

emargarida · Rookie Joined: 17 Dec 2010 Posts: 7 Location: London

Hi,

I seen unable to solve this problem, could anyone help me?

"An object is dropped from a height h and strikes ground with a velocity v. If the object is dropped from a height of 2h, which of the following represents its velocity when it strikes the ground?"

Thanks

emargarida · Rookie Joined: 17 Dec 2010 Posts: 7 Location: London

the options go:

a) v

b) 1.4v

c) 2v

d) 4v

Thanks

cat2devnull · Regular Joined: 23 Jul 2010 Posts: 23 Location: Adelaide

You need to have your head around the equations of motion so start by looking them up on wikipedia and also look at the Khan Academy projectile motion videos.

v^2 = u^2 + 2as

where
s = the distance between initial and final positions (height)
u = the initial velocity = 0
v = the final velocity
a = the constant acceleration (gravity)

Thus:
v^2=2as
or another way of looking at it is:
v^2=2gh (gravity and height)
or
v=√2gh

So if you double the height then you get;

v=√4gh

Aka you multiply v by √2 or 1.4 hence option b.

You can actually calculate this properly by building the two equations and substituting one into the other using the common var of gravity but you will run out of time in the exam if you actually were to do this.

v^2=2gh

g=v^2/2h

thus if you look at the two scenarios (using capital v and h for the second experiment where H=2h);

g=v^2/2h and g=V^2/2H

so

v^2/2h = V^2/2H

since H=2h

v^2/2h = V^2/4h

now you can cancel out the h

v^2/2 = V^2/4

multiply both sides by 4 to get rid of the denominator

2v^2 = V^2

square root both sides to get rid of the square

V = v√2

Ta da! the new Velocity is √2 (or 1.4) times the old velocity.

emargarida · Rookie Joined: 17 Dec 2010 Posts: 7 Location: London

thank you very much!!! That was extremely helpful. Very Happy