Need help starting a vector lab, can someone please help?

[amzfishman]

I'll try to explain this as clearly as I can, but there's a lot of information that has yet to be put together. I'll do my best.

Basically, I have to calculate the angle at which I need to release 2 bowling balls down a ramp (one ball is moving at 1.696 m/s and the other moving at 1.126 m/s) to have the 2 balls hit each other. The set up is described in the diagram below.The problem I'm running into is that in order to figure out when these vectors intersect, I have to know the angle between the vectors, but to get the angle between the vectors I have to know where they intersect. I also need to be able to describe both vectors.

I don't want the answer spelled out for me, but can someone please just point me in the right direction? Thank you so much.

 

[chalaman1403]

Amzfishman,

You are told that the first balls moves at a certain speed in the positive x direction, remember the cinematics equations.
\(\displaystyle x(t) = x_0 + v_0*t \)
\(\displaystyle v(t) = v_0 \)
that is for a constant speed \(\displaystyle v_0 \) and \(\displaystyle x_0 \) is where the ball is at t=0, you have the freedom to choose that point to be 0, so you will be
setting the origin of your coordinate system there.
The other ball moves with a similar motion in the x direction, you should use sine or cosine to determine the speed on that direction, and choose the \(\displaystyle x_0\) consistent with your coordinate system (if you put the origin where the other ball is, this one will be at x=12.72 at t=0.
You also know the movement in the y direction of the second ball. You can evaluate at the time they cross, you will have the same x coordinate for both and the y coordinate will be either 0 or 5.41, depending on where you put the y=0 in your coordinate system.
You will get a system of 2 equations with the angle and the time as variables and you should be able to solve it.
Regards,
Damián Vallejo.

 

[Deleted member 4993]

I'll try to explain this as clearly as I can, but there's a lot of information that has yet to be put together. I'll do my best.

Basically, I have to calculate the angle at which I need to release 2 bowling balls down a ramp (one ball is moving at 1.696 m/s and the other moving at 1.126 m/s) to have the 2 balls hit each other. The set up is described in the diagram below.The problem I'm running into is that in order to figure out when these vectors intersect, I have to know the angle between the vectors, but to get the angle between the vectors I have to know where they intersect. I also need to be able to describe both vectors.

I don't want the answer spelled out for me, but can someone please just point me in the right direction? Thank you so much.View attachment 2892

Let's assume Ball#1 (B_1) starts at O and travels along x-axis

Ball#2 (B_2) starts at T and travels along a path making an angle Θ with x-axis

B_1 & B_2 collides at a point P on the x-axis at a time 't'.

Then

OP = 12.72 - TP*cos(Θ) = 1.696 * t

TP = 1.126*t

and

5.41 = TP*sin(Θ)

then

1.126*t*cos(Θ) = 12.72 - 1.696 * t

1.126*t*sin(Θ) = 5.41

then

(1.126 * t)² = (12.72 - 1.696 * t)² + (5.41)²


Solve for 't' and solve for "Θ".