Projectile Motion: Determining Height of Wood Chips Ejected at 30 degrees

[Milkster18]

Hi I'm new to the physics forum as this is my first post so apologies for any mistakes.

I have a question relating to projectile motion that i don't understand the question is:

The chipping machine is designed to eject wood chips at Ui = 7.6 m/s. If the tube is oriented at 30 degrees from the horizontal, determine how high, h, the chips strike the pile if they land on the pile 6m from the tube. ( origin of chipping machine ejecting wood chips is 2m above ground)

the answer is 1.4m but i can't figure out how to get this answer.

Any help relating to this will be much appreciated.

 

[Doc Al]

Try this:
(1) How long does it take for the chips to travel the 6m to the pile?
(2) In that amount of time, how high do the chips rise?

 

[eshaw]

You have to show some work before people will help you in more detail. Here are some starting tips though: split up the velocity into x and y components of the velocity and then use those values to figure out the answer to the two questions Doc Al posed.

 

[Milkster18]

for (1)

Uy = 7.6 sin 30
Uy = 3.8 m/s

use equation: Sy = (uy)t - 0.5(9.81)t^2

2 = (3.8)t - 0.5(9.81)t^2

is this correct so far to find time?

 

[Doc Al]

for (1)

Uy = 7.6 sin 30
Uy = 3.8 m/s

use equation: Sy = (uy)t - 0.5(9.81)t^2

2 = (3.8)t - 0.5(9.81)t^2

is this correct so far to find time?

You are looking at the vertical component of the motion, which is what you need for part 2. What you have is almost right for height (vertical position) as a function of time. Your equation should be:
Sy = y₀ + (uy)t - 0.5(9.81)t^2

But first you need to find the time. For that, analyze the horizontal motion.

 

[Milkster18]

horizontal motion :

use equation: Sx = Ux t

So : t = Ux / Sx

t = 6.58 / 6 = 1.096 s ? is that correct?

 

[Doc Al]

horizontal motion :

use equation: Sx = Ux t

Good!

So : t = Ux / Sx

Not quite. Careful when you solve for t.

t = 6.58 / 6 = 1.096 s ? is that correct?

Not yet. Fix your error above and you'll be fine.

 

[Milkster18]

oh wow i done it thanks a lot :P !

but i won't just leave without a thanks i'll explain what i did in the end.

So : t = Sx / Ux

t = 6 / 6.58 = 0.911s (re-arranging equations isn't my strong point)

Sy = 2 + (3.8)0.911 - 0.5 (9.81)(0.911)^2
Sy = 5.46 - 4.07
Sy = 1.39m ~ 1.4m

thanks a lot Doc Al, now i understand what to do :)

 

[Doc Al]

Excellent!