Simple question on 2d projectiles

1. Dec 16, 2014

HMPARTICLE

1. The problem statement, all variables and given/known data
A catapult projects a stone in the normal direction to a playground which slopes at a angle of 10 degrees to the horizontal.
The initial speed of the stone is 18 m/s. calculate the range parallel to the playground.

2. Relevant equations
the usual ones!

3. The attempt at a solution

My first equation is v = 18cos10i + 18sin10j
using v = u + at in the y direction with a = -9.8m/s^2 and v = 0 u =18sin10
using this i find that the time that the stone hits the ground is t = 0.32 seconds
now in the x direction x = vt since we ignore air resistance
i obtain 18cos10(0.32) = 5. 8 m

the answer in the back of the book is 11.8 m.

so i am wrong. i think i have interpreted the question incorrectly!
but i have tried setting the angle to 80 degrees, but that came out horribly wrong

2. Dec 16, 2014

haruspex

Where i is horizontal? No. A useful check is to consider what cos theta and sin theta give when theta = 0. In this case, that means a horizontal playground, so the stone goes straight up.
When considering the final speed of a projectile, you must take the speed just before it hits whatever it hits. The speed after it has landed is irrelevant.

3. Dec 16, 2014

TSny

Does the initial velocity vector make a 10 degree angle to the horizontal?
Looks like you are finding the time at which the vertical component of velocity is zero. Is this the time that you want to use for when the stone returns to the ground?

Also, note that the stone does not return to the same vertical height as it started due to the tilt of the playground.

I think things will work out more easily if you choose your coordinate system such that the x-axis runs down along the slope of the playground and the y-axis is perpendicular to the ground of the playground.

Attached Files:

• Proj slope.png
File size:
1.3 KB
Views:
71
4. Dec 16, 2014

HMPARTICLE

if i was to use the suggested co-ordinate system wouldnt the cannon just fire at a 90 degree angle?

5. Dec 16, 2014

TSny

Yes, the cannon would fire at a 90 degree angle with respect to the x-axis running along the slope. If you do decide to choose your x-axis parallel to the slope and the y-axis perpendicular to the slope, then you will want to think about the x and y components of acceleration of the stone.

6. Dec 16, 2014

HMPARTICLE

DONE! Thank you so much guys!