Kinematics: Angled Projectile Launch

[SlooM]

Homework Statement

Determine the initial velocity of the projectile as it comes out of a cannon at a 20° angle.

Homework Equations

d = (Vi)(t) + 1/2(a)(t)^2

The Attempt at a Solution

I've split the question into both x and y components and solved for both using the equation above. Although I'm honestly unsure if I'm doing this correctly, would like some verification on my answer and point out any mistakes. Much appreciated! (Image below)

http://imgur.com/pPWO2jG

 

[Sunil Simha]

Hi SlooM,

Are you sure v_0y is 0 in the first equation that you've used to find t?

 

[SlooM]

Ah, I think that may have been my mistake which is kind of why I look at it and it doesn't make sense. I just put 0 for v0y and assumed it canceled that half of the equation. What would I put though, I feel like I don't have enough variables and am super confused.

 

[Bashkir]

In addition to what Sunil has stated, there was also an algebra mistake at the end preventing you from getting the correct answer.

$$\cos\theta = \frac{v_x}{v_i}$$

to

$$(cos\theta)v_x = v_i$$

instead of

$$v_i =\frac{v_x}{cos\theta}$$


An easier way to do this problem it to remember that your x-component of velocity already has a cosine term in it. So once you solve for time you can simply say

$$x(t) = V_otcos\theta$$

 

[SlooM]

Oh! I can't believe I didn't see that. So I redid the algebra at the end and got 44.5 m/s but are my calculations in the previous x and y calculations correct? I keep second guessing myself :/

I'm a rookie at physics but trying to improve. I appreciate all of your help and it means a lot.

 

[Sunil Simha]

Oh! I can't believe I didn't see that. So I redid the algebra at the end and got 44.5 m/s but are my calculations in the previous x and y calculations correct? I keep second guessing myself :/

I'm a rookie at physics but trying to improve. I appreciate all of your help and it means a lot.

Hey we are all rookies

We get two equations right?

$-1.5= v_{0y}t + \frac{g}{2}t^2$
$23=v_{0x}t$

All we have to do is eliminate t. Moreover, v_0x and v_0y are related. So, you should be able to find v_0x explicitly (and hence v_0y).

Could you check you answer again? I seem to be getting something different.