# Moving Particle Equation

• May 20th 2008, 12:05 AM
Simplicity
Moving Particle Equation
Q: With the following two equations, find the value of $\displaystyle u$:
$\displaystyle 2ut = 735 \ \ \ \ \ \ \ \ \ \ \ \ \dots (1)$
$\displaystyle 0 = 3ut - 21 gt^2\ \ \ \ \dots (2)$.

The correct answer is $\displaystyle u=24.5$. I'm getting an incorrect answer. Can someone do this question and see if they obtain the correct answer so I can compare with mine. Thanks in advance.
• May 20th 2008, 12:45 AM
mr fantastic
Quote:

Originally Posted by Air
Q: With the following two equations, find the value of $\displaystyle u$:
$\displaystyle 2ut = 735 \ \ \ \ \ \ \ \ \ \ \ \ \dots (1)$
$\displaystyle 0 = 3ut - 21 gt^2\ \ \ \ \dots (2)$. Mr F adds: => 0 = ut - 7gt^2.

The correct answer is $\displaystyle u=24.5$. I'm getting an incorrect answer. Can someone do this question and see if they obtain the correct answer so I can compare with mine. Thanks in advance.

Substitute ut from (1) into (2), take g = 9.8 and solve for t (keeping only the positive value): t = 2.31 seconds.

Substitute t into (1) and solve for u: u = 159.1 metres.

Then again, I'm terrible with arithmetic ....
• May 20th 2008, 02:20 AM
Simplicity
Quote:

Originally Posted by mr fantastic
Substitute ut from (1) into (2), take g = 9.8 and solve for t (keeping only the positive value): t = 2.31 seconds.

Substitute t into (1) and solve for u: u = 159.1 metres.

Then again, I'm terrible with arithmetic ....

But that contradicts the marks scheme answer as $\displaystyle u=24.5$. (Worried)
• May 20th 2008, 03:36 AM
Isomorphism
Quote:

Originally Posted by Air
But that contradicts the marks scheme answer as $\displaystyle u=24.5$. (Worried)

Could you completely specify the problem (as in originally how it was stated)?
I think that will help(Thinking)
• May 20th 2008, 03:47 AM
Simplicity
Quote:

Originally Posted by Isomorphism
Could you completely specify the problem (as in originally how it was stated)?
I think that will help(Thinking)

Q:
A particle $\displaystyle P$ is projected with velocity $\displaystyle (2u \b{i} + 3u \b{j}) \ \text{ms}^{-1}$ for a point $\displaystyle O$ on a horizontal plane, where $\displaystyle \b{i}$ and $\displaystyle \b{j}$ are horizontal and vertical unit vectors respectively. The particle $\displaystyle P$ strikes the plane at a point $\displaystyle A$ which is $\displaystyle 735m$ from $\displaystyle O$.

Show that $\displaystyle u=24.5$.
• May 20th 2008, 03:56 AM
Isomorphism
Quote:

Originally Posted by Air
Q: With the following two equations, find the value of $\displaystyle u$:
$\displaystyle 2ut = 735 \ \ \ \ \ \ \ \ \ \ \ \ \dots (1)$
$\displaystyle 0 = 3ut - 21 gt^2\ \ \ \ \dots (2)$.

The correct answer is $\displaystyle u=24.5$. I'm getting an incorrect answer. Can someone do this question and see if they obtain the correct answer so I can compare with mine. Thanks in advance.

Well why did you write the second equation like that?

The correct equation is

$\displaystyle 0 = 3ut - \frac12 gt^2$

And I solved it to get $\displaystyle u=24.49$