Kinematics 2D: Solve Initial Speed of Cork

[to819]

Homework Statement

A cork shoots out of a champagne bottle at an angle of 38.0 degrees above the horizontal. If the cork travels a horizontal distance of 1.4m in 1.15 seconds what was the initial speed?

Homework Equations

x(t)=x₂+v_it+.5at²

The Attempt at a Solution

1.4=0+1.15x

x=1.217

However, this is wrong, hence the asking for help. I'm really wondering if I'm using the wrong formula or just missing something obvious.

 

[dotman]

Hello,

Yeah, like you said, that's wrong :P

Your formula is the right idea though. Usually with this problem, they tell you something like, "A ball is shot out of a cannon at an angle x with an initial speed of v0. How long does it take to hit the ground, and how far does it go?" And then you work through it by calculating the y component of the motion (which is affected only by gravity) to find the time, and then plug that time into the x version of the equation to find the distance. Because the full equation is:

s(t) = s0 + v0t + 1/2at^2 , which you can break down into the x and y components:

y(t) = y0 + v0yt + 1/2ayt^2 and
x(t) = x0 + v0xt +1/2axt^2,

where you know that the acceleration in the y-axis is due solely to gravity (ay = g), and the acceleration in x is 0 (these problems typically neglect friction).

Here, however, you've been given the angle, the horizontal distance, and the time already, and all you have to do is find the initial speed.

Your solution is incorrect because you neglected the y component of the motion. IE, you solved your equation for the x component only, as if it had been shot at an angle of zero and there were no gravity.

A clue for you should have been (probably was, but you weren't sure what to do with it) the fact that you didn't use the 38 degrees anywhere. You will need this number.

Hope this helps, write again if you're not sure how to proceed!