# Classic Hit and Stick momentum?

## Homework Statement

Three balls of clay have masses m1 = 106 g, m2 = 148 g, m3 = 120 g, and speeds v1 = 1.48 m/s, v2 = 1.19 m/s, v3 = 1.85 m/s. They move in the directions: (1) at 45° from the horizontal, (2) horizontally left, and (3) vertically up. They collide simultaneously and stick together. Calculate the speed and the direction (angle) of the resulting blob of clay.

p=mv

## The Attempt at a Solution

Vx = 106 * 1.48 * cos(45) - 148 * 1.19 = -65.189882 m/s

Vy = 106*1.48sin(45) + 120*1.85 = 332.0309 m/s

V = sqrt(332.0309^2 + [-65.189882]^2) (answer?)

angle = arctan (Vy/Vx)

This isn't right is it,

Andrew Mason
Homework Helper

## Homework Statement

Three balls of clay have masses m1 = 106 g, m2 = 148 g, m3 = 120 g, and speeds v1 = 1.48 m/s, v2 = 1.19 m/s, v3 = 1.85 m/s. They move in the directions: (1) at 45° from the horizontal, (2) horizontally left, and (3) vertically up. They collide simultaneously and stick together. Calculate the speed and the direction (angle) of the resulting blob of clay.

p=mv

## The Attempt at a Solution

Vx = 106 * 1.48 * cos(45) - 148 * 1.19 = -65.189882 m/s

Vy = 106*1.48sin(45) + 120*1.85 = 332.0309 m/s

V = sqrt(332.0309^2 + [-65.189882]^2) (answer?)

angle = arctan (Vy/Vx)

This isn't right is it,
First of all we have to know the direction of the 45° ball. Is it 45° to the left or to the right?

It is not clear what you are doing in calculating vx and vy.

I suggest you write out the equations for momentum before and after the collision and then relate them. How are they related?

AM

• 1 person
No that isn't right, remember that the conservation of momentum applies, use it. Calculate the total momentum in the x direction before the collision, then it them equal to the total momentum in the x direction after the collision, then do the same for the y direction. Then you will have two equations with two unknowns, use algebra to solve for both. What you did was incorrect, you cannot find the total momentum in the x direction and set it equal to the velocity in the x direction. If in doubt, check the units.

• 1 person
So

mv = m1 * v1 + m1*v2 + m2*v3? in the x and y directions then use trig to find speed and direction?

haruspex
Homework Helper
Gold Member
2020 Award
So

mv = m1 * v1 + m1*v2 + m2*v3? in the x and y directions then use trig to find speed and direction?
Yes. What you calculated in the OP (assuming m1 was moving up and to the right, which is not clear) were the x and y momenta, not the x and y speeds. You just needed to divide by the combined mass.

• 1 person
Cool, I got it!