A 400g soccer ball is moving through the air at 3.57m/s [64.8°W of N] horizontally at the top of its flight.

If at that instant, the soccer ball is struck by a 450g crocket ball moving at 5.46m/s [N], and the soccer ball flies off at 4.28m/s[22.4°W of N]. What will be the velocity of the crocket ball immediately after the collision?
| what is the final impulse of the crocket ball in the northward direction?
|| what is the final impulse of the soccer ball in the westward direction?

64.8o W of N = 154.8o CCW.

22.4o W of N. = 112.4o CCW.

M1*V1 + M2*V2 = = M1*V3 + M2*V4.
0.4*3.57m/s[154.8o] + 0.45*5.46m/s[90o]
= 0.4*4.28m/s[112.4o] + 0.45*V4.
1.43m/s[154.8] + 2.46m/s[90o] = 1.71m/s[112.4] + 045V4,
-1.29+0.609i + 2.46i = -0.652+1.58i + 0.45V4,
-1.29 + 3.07i = -0.652 + 1.58i + 0.45V4,
-0.638 + 1.49i = 0.45V4,
V4 = -1.42 + 3.31i = 3.60m/s[-66.8o] = 3.60m/s[66.8o N of W].
= Velocity of crocket ball.

To find the velocity of the crocket ball immediately after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Let's first calculate the total initial momentum. The momentum of an object is given by the product of its mass and velocity.

The initial momentum of the soccer ball is given by:
Momentum_soccer_ball_initial = mass_soccer_ball * velocity_soccer_ball_initial

Given:
mass_soccer_ball = 400g = 0.4kg
velocity_soccer_ball_initial = 3.57m/s [64.8°W of N]

Let's break down the initial velocity of the soccer ball into its components:
velocity_soccer_ball_initial_W = velocity_soccer_ball_initial * cos(64.8°)
velocity_soccer_ball_initial_N = velocity_soccer_ball_initial * sin(64.8°)

Now let's calculate the initial momentum of the soccer ball using the components:
Momentum_soccer_ball_initial = mass_soccer_ball * velocity_soccer_ball_initial_W

Using the given values:
Momentum_soccer_ball_initial = 0.4kg * 3.57m/s * cos(64.8°)

Next, let's calculate the momentum of the crocket ball initially:
Momentum_crocket_ball_initial = mass_crocket_ball * velocity_crocket_ball_initial

Given:
mass_crocket_ball = 450g = 0.45kg
velocity_crocket_ball_initial = 5.46m/s [N]

Momentum_crocket_ball_initial = 0.45kg * 5.46m/s

The total initial momentum is the sum of the momenta of both objects:
Total_initial_momentum = Momentum_soccer_ball_initial + Momentum_crocket_ball_initial

To find the velocity of the crocket ball immediately after the collision, we can use the total initial momentum and the total final momentum (since momentum is conserved):

Total_initial_momentum = Total_final_momentum

Given:
Total_final_momentum = Momentum_soccer_ball_final + Momentum_crocket_ball_final

Let's find the final momentum of the soccer ball using the given information:
velocity_soccer_ball_final = 4.28m/s [22.4°W of N]

First, let's break down the final velocity of the soccer ball into its components:
velocity_soccer_ball_final_W = velocity_soccer_ball_final * cos(22.4°)
velocity_soccer_ball_final_N = velocity_soccer_ball_final * sin(22.4°)

Next, let's calculate the final momentum of the soccer ball using the components:
Momentum_soccer_ball_final = mass_soccer_ball * velocity_soccer_ball_final_W

Using the given values:
Momentum_soccer_ball_final = 0.4kg * 4.28m/s * cos(22.4°)

Finally, we can calculate the final momentum of the crocket ball:
Momentum_crocket_ball_final = Total_final_momentum - Momentum_soccer_ball_final

To find the final impulse of the crocket ball in the northward direction, we can calculate the change in momentum:

Impulse_crocket_ball_final_N = Momentum_crocket_ball_final - Momentum_crocket_ball_initial

Substituting the values, we can find the final impulse of the crocket ball in the northward direction.

Similarly, to find the final impulse of the soccer ball in the westward direction, we can calculate the change in momentum:

Impulse_soccer_ball_final_W = Momentum_soccer_ball_final - Momentum_soccer_ball_initial

Substituting the values, we can find the final impulse of the soccer ball in the westward direction.