Projectile Motion Problem: Calculating Distance and Velocity

[jill2040]

1. A small steel ball bearing with a mass of 27.0 g is on a short compressed spring. When aimed vertically and suddenly released, the spring sends the bearing to a height of 1.17 m. Calculate the horizontal distance the ball would travel if the same spring were aimed 34.0° from the horizontal.



2. I've tried the whole problem from every direction I can think of but I keep getting it wrong. Can anyone tell me step by step what I would need to do? I don't need answers, just directions with concepts.



3. I assume the first thing I need to do is find the initial velocity. I found what the final velocity would be if the bearing was dropped from 1.17 m to be -4.7887 m/s. I found that number no matter what[ equation I used. From there, I found the total time of motion to be .9772 s. I multiplied the t times the initial v times cos(34) and got 3.88 m but the homework program still told me I was wrong. I'm missing something.

 

[gneill]

Can you detail how you found your "total time of motion"?

 

[jill2040]

I used t=v/g and doubled it to account for the bearing coming back down.

 

[gneill]

I think you'll want to calculate the time of flight for the case when the ball bearing is launched at an angle. Time of flight will vary with angle.

 

[jill2040]

How would I go about that? I tried t=(4.7887 m/s * sin(34)/9.8 m/s^2 but that didn't seem to get me anywhere.

 

[gneill]

Go back to the general equation of motion for the y-component of the motion.

y = v*t - (1/2)gt^2

You have a velocity for the y-component, and the flight ends when y = 0. Solve for t.