# projectile help

• Nov 11th 2008, 09:48 AM
khuezy
projectile help
Hi, a projectile is fired with an initial speed of 500 m/s and angle of elevation 30 degrees.
Find the range of the projectile, the max height, and speed at impact

Thanks.
• Nov 11th 2008, 11:56 AM
Arch_Stanton
Firstly, we need to compute the component velocities.
$\displaystyle v_y=v_0 sin \alpha$
$\displaystyle v_x=v_0 cos \alpha$
and duration of this movement:
$\displaystyle v_y=gt \Rightarrow t=\frac{v_y}{g}$
Maximum height is: $\displaystyle h=\frac{gt^2}{2}=\frac{v_y^2}{2g}=\frac{v_0^2sin^2 \alpha}{2g}$
The rage: $\displaystyle x=v_xt=v_0cos\alpha \frac{v_0sin \alpha}{g}=\frac{v_0^2sin \alpha cos\alpha}{g}$
The speed at impact is equal the initial speed.
• Nov 12th 2008, 02:34 PM
khuezy
hmm
what am I doing wrong w/ the range?
I'm getting a 11km rather than 22km(book)
• Nov 12th 2008, 03:06 PM
skeeter
because the correct range equation is ...

$\displaystyle \frac{2v_0^2 \cdot \sin{\theta}\cos{\theta}}{g} = \frac{v_0^2 \cdot \sin(2\theta)}{g}$
• Nov 12th 2008, 03:33 PM
khuezy
thank you
!