# Finding Speed of Projection for Two Balls Collision

• whiteman
In summary: Hi whiteman, it is not clear how you arrived at your expressions for Ua and Ub. It is best to show your steps and calculations so others can check for errors. In any case, the correct expressions should be:Ua = (gcosB)/sin(A-B)Ub = (2gcosA)/sin(A-B)Plugging these into the equations for x and y distances, we can solve for the speed of projection for the two balls.
whiteman

## Homework Statement

A ball was projected at an angle A to the horizontal. One second later another ball was projected from the same point at an angle B to the horizontal. One second after the second ball was released, the two balls collided. Find the speed of projection for the two balls.

s = ut + 1/2 at2

## The Attempt at a Solution

In x-direction:
sA = ua cosA t
sB = ub cosB (t-1)

In y-direction:
sA = ua sinA t -1/2 gt2
sB = ub sinB (t-1) -1/2 g(t-1)2

When they collide the distances they traveled in the x and y directions are equal to each other at t=2. I tried to solve for ua and ub but got stuck.

Hi whiteman, welcome to PF.
When the balls collide, ball A is in the air for 2 s and ball B is in the air for 1 s.
For them x distance is the same. So
2*Ua*cosA = Ub*cosB -----(1)
For y
2*Ua*sinA - 1/2*g*(2)^2 = Ub*sinB - 1/2*g -------(2)
From eq.(1), find the expression for Ub and substitute it in equation (2) and solve for Ua.

Hi, thanks for the welcome.
Is Ua and Ub meant to expressed in terms of cos/sin of A/B or are they just numbers?
I got Ua = 3gcosB/4sin(A+B) and Ub = 3gcosA/2sin(A+B).
Is this right or am I going wrong?

In the expression of Ua and Ub sin(A-B) should be there instead of sin(A+B)

## 1. What is the formula for finding the speed of projection for two balls collision?

The formula for finding the speed of projection for two balls collision is:
v = (m1u1 + m2u2)/(m1 + m2)
where v is the final velocity, m1 and m2 are the masses of the two balls, and u1 and u2 are the initial velocities of the two balls.

## 2. What is the significance of finding the speed of projection for two balls collision?

Finding the speed of projection for two balls collision allows us to understand the behavior of objects in motion and their interactions with each other. It also helps us determine the outcome of a collision and whether it is elastic or inelastic.

## 3. Can the speed of projection for two balls collision be negative?

Yes, the speed of projection for two balls collision can be negative. This indicates that the direction of the velocity is opposite to the direction of the initial motion.

## 4. How does the angle of projection affect the speed of projection for two balls collision?

The angle of projection affects the speed of projection for two balls collision by determining the direction of the velocity. A higher angle of projection will result in a higher velocity in the vertical direction, while a lower angle will result in a lower velocity.

## 5. What other factors can affect the speed of projection for two balls collision?

Other factors that can affect the speed of projection for two balls collision include the surface on which the collision occurs, the elasticity of the balls, and any external forces such as friction or air resistance.

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