- #1

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## Homework Statement

Conveyor belt A, which forms a 20° angle with the horizontal, moves at a constant speed of 4 ft/s and is used to load an airplane. Knowing that a worker tosses duffel bag B with an initial velocity of 2.5 ft/s at an angle of 30° with the horizontal, determine the velocity of the bag relative to the belt as it lands on the belt.

## Homework Equations

V

_{i,x}= V

_{i}*cos([tex]\theta[/tex])

V

_{i,y}= V

_{i}*sin([tex]\theta[/tex])

(x

_{f}-x

_{i}) =V

_{i,x}*t

(y

_{f}-y

_{i}) =V

_{i,y}*t - (1/2)*g*t

^{2}

r

_{B}= r

_{A}+r

_{B/A}

v

_{B}= v

_{A}+v

_{B/A}

a

_{B}= a

_{A}+a

_{B/A}

## The Attempt at a Solution

I think I've gotten the majority of this problem tackled, so I will list what I have done (as I am highly likely to have done something wrong.) As you can see from the picture below, a linear equation (I think?) is required out of the conveyor belt, so that is the first thing I did.

We know that to make a right triangle with the belt, one side is 90, we're given 20, so the final angle is 70. For pure relations' sake to find a slope, I set the bottom length equal to 10, used tan(20)=opp/10, and found the rise/run to be 3.64/10 which came out to be a slope of .364.

I also set my origin at the location of the duffel bag, which was 1.5 feet above the starting location of the conveyor belt line. So, for my linear equation, I found y=.364x-1.5

Then from there, (I think this is right?) I subbed my x

_{f}and y

_{f}equations into my linear equation. I was then faced with a quadratic, which, when solved for t, I found t=.3209 s. Fast forwarding a bit more after this I found my final x and y distances.

My x final distance was .6947 ft, while my y final distance was -1.2465 ft.

And...this is where I taper off. I am unsure how to proceed next. I know my final distances, the time it took to hit the conveyor belt...but I am not sure how to relate all of this to find the relative velocity of the bag to the belt.

Could anyone spare some help? I would greatly appreciate it!

**4. F.B.D.**