A hockey puck B rests on frictionless, level ice and is struck by a second puck A, which was originally traveling at 40.0 m/s and which is deflected 30 degrees from its original direction. Puck B acquires a velocity at a -45 degree angle to the original direction of A. The pucks have the same mass.

a) compute the speed of each puck after the collision
b) what fraction of the original kinetic energy of puck A dissipates during the collision

a) Well, let's break some ice here. Since there's no friction, we can conserve momentum in the x and y directions separately.

In the x-direction:
Initial momentum = Final momentum

Puck A = mass * velocity of A * cos(30)
Puck B = mass * velocity of B * cos(-45)

Putting in the values:
mass * 40 m/s * cos(30) = mass * velocity of B * cos(-45)

Now in the y-direction:
Initial momentum = Final momentum

Puck A = mass * velocity of A * sin(30)
Puck B = mass * velocity of B * sin(-45)

Putting in the values:
mass * 40 m/s * sin(30) = mass * velocity of B * sin(-45)

Solving these equations will give us the velocities of both pucks after the collision.

b) Now, let's talk about dissipating energy. The fraction of the original kinetic energy that dissipates during the collision can be found by comparing the final kinetic energy of puck A with its initial kinetic energy.

The equation for kinetic energy is:
Kinetic energy = (1/2) * mass * velocity^2

So, we calculate the initial and final kinetic energies of puck A and find the ratio to determine the fraction that dissipates.

Remember, this is just a hockey problem, not a stand-up routine. But we'll still try to keep it puckin' funny!

To compute the speed of each puck after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.

a) Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Since the pucks have the same mass, we can simplify this calculation.

Let's denote the initial velocity of puck A as vA and the initial velocity of puck B as vB. The final velocities of both pucks after the collision will be denoted as v'A for puck A and v'B for puck B.

From the conservation of momentum:
m * vA = m * v'A + m * v'B

Since the pucks have the same mass, 'm' cancels out:
vA = v'A + v'B

Now, let's consider the angle of deflection. We know that puck A is deflected by 30 degrees from its original direction, and puck B acquires a velocity at a -45 degree angle to the original direction of A.

Using trigonometric identities, we can calculate the horizontal and vertical components of the velocities:

For puck A:
vAx = vA * cos(30)
vAy = vA * sin(30)

For puck B:
vBx = vB * cos(-45)
vBy = vB * sin(-45)

Now, let's substitute these values into the conservation of momentum equation:

vA * cos(30) = v'A * cos(30) + v'B * cos(-45)
vA * sin(30) = v'A * sin(30) - v'B * sin(-45)

Now we have a system of two equations with two unknowns (v'A and v'B). We can solve these equations to find the values of v'A and v'B.

Next, to compute the speed of each puck, we can use the Pythagorean theorem:

For puck A:
speedA = sqrt((v'A)^2 + (vAy)^2)

For puck B:
speedB = sqrt((v'B)^2 + (vBy)^2)

b) To calculate the fraction of the original kinetic energy of puck A that dissipates during the collision, we'll compare the initial kinetic energy (KEi) of puck A to its final kinetic energy (KEf).

The kinetic energy equation is given by:
KE = (1/2) * m * v^2

Therefore, the initial kinetic energy of puck A is:
KEi = (1/2) * m * vA^2

And the final kinetic energy of puck A is:
KEf = (1/2) * m * (v'A)^2

The fraction of kinetic energy dissipated can be calculated as:
Fraction of energy dissipated = (KEi - KEf) / KEi

a)Let final speed of A be v1, and final speed of B be v2.Using conservation of momentum, consider the horizontal:

40m = v1*cos30 + v2*cos45

and the vertical

0 = v1*sin30 + v2*sin45

In second equation, express v1 in terms of v2, then substitute into the first equation to find v2. v1 is found in similar way.

b) From a), u have the value of v1. Calculate the fraction (v1*v1)/(40*40)

V1= 25.4

v2=14.6