project motion problem

[denisa]

If increasing the initial speed of a projectile by a factor of 5 increases its rane by what factor? Assume the elevation is the same.

Possible answers:
a)factor of 25
b)factor of 5
c)factor of 2.24
d) The elevation must be specified before an answer can be found

I know the Range formula=((v0^2)/g)sin2a
Have problem with this problem... Help me please. Anything will help.. Thanks

 

[Unknown008]

Keeping the angle constant, means that sin(2a) remains constant, right?

\(\displaystyle Range = \frac{v_o\ ^2 \sin(2a)}{g}\)

So, this becomes:

\(\displaystyle Range = \frac{v_o\ ^2k}{g}\)

g is also constant, so we can combine those two constants to give another constant. Let's call it c.

\(\displaystyle Range = c v_o\ ^2\)

You can then set up the proportionality symbol:

\(\displaystyle Range \propto v_o\ ^2\)

Can you work with this one now?

 

[denisa]

ok, is it means that @ stands for angle? (which i don't have)?

 

[denisa]

ok is @ means the angle of object? ( which i do not have?) Right?

 

[denisa]

ok, i know that v0 is a speed, but i don't know the speed? if i use 5 as a speed it will give me 25..? Please help me..

 

[Unknown008]

Not quite the way you do it.

The first 'throw' gives a certain range for a velocity of throw v0:

\(\displaystyle R \propto v_0\ ^2\)

This means that:

\(\displaystyle \frac{R}{v_0\ ^2} = k\)

So, no matter what the velocity or the range, they will still give the constant k.

Now, you increase v0 by a factor of 5. This means, \(\displaystyle v_o \rightarrow 5v_o\)

The new range, R' is then:

\(\displaystyle \frac{R'}{(5v_o)^2} = k\)

But we can write down k as the previous equation!

\(\displaystyle \frac{R'}{(5v_o)^2} = \frac{R}{v_o\ ^2}\)

Now, you simplify a little:

\(\displaystyle \frac{R'}{25v_o\ ^2} = \frac{R}{v_o\ ^2}\)

\(\displaystyle \frac{R'}{25} = R\)

\(\displaystyle R' = 25R\)

So, the resultant range R' is 25 times the initial range, R

 

[denisa]

ok i understand. Thank you very much!!!!!

 

[Unknown008]

I'm glad you do! Feel free to ask any more questions when you have doubts!