An impulse of 25 N*s is exerted on a 0.25 kg baseball traveling 40 m/s west. What is the velocity of the baseball after it has been hit?

To find the velocity of the baseball after it has been hit, we can use the principle of conservation of momentum. This principle states that the total momentum of a system before an event is equal to the total momentum after the event, assuming there are no external forces acting on the system.

The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is calculated as:

p = m * v

Where:
p = momentum
m = mass of the object
v = velocity of the object

In this case, the baseball has a mass of 0.25 kg and is initially traveling at a velocity of 40 m/s west. The impulse exerted on the baseball is 25 N*s.

Impulse (J) is defined as the change in momentum of an object and is given by the formula:

J = Δp = m * Δv

Where:
J = impulse
Δp = change in momentum
m = mass of the object
Δv = change in velocity

In this case, the impulse is given as 25 N*s. Therefore, we can rewrite the equation as:

25 N*s = 0.25 kg * Δv

Now, we can solve for Δv:

Δv = 25 N*s / 0.25 kg
= 100 m/s

The change in velocity (Δv) is 100 m/s.

To find the final velocity (v_f) after the baseball has been hit, we can use the formula:

v_f = v_i + Δv

Where:
v_f = final velocity
v_i = initial velocity
Δv = change in velocity

In this case, the initial velocity (v_i) is given as 40 m/s west. Substituting the values, we get:

v_f = 40 m/s + 100 m/s
= 140 m/s west

Therefore, the velocity of the baseball after it has been hit is 140 m/s west.