Before a collision, a 27 kg object is moving at +11 m/s. Find the impulse that acted on the object if, after the collision, it moved at the following velocities.

a. 8 m/s
b. -8m/s

To find the impulse that acted on the object, we can use the impulse-momentum principle, which states that the impulse acting on an object is equal to the change in momentum.

The change in momentum (∆p) is given by the equation:

∆p = m * ∆v

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

a. With a velocity of 8 m/s:
∆v = 8 m/s - 11 m/s = -3 m/s (since the object's velocity decreased)

Now we can calculate the impulse (∆p) by multiplying the mass (m) by the change in velocity (∆v):

∆p = 27 kg * (-3 m/s) = -81 kg·m/s

Therefore, the impulse that acted on the object when it moved at 8 m/s after the collision is -81 kg·m/s.

b. With a velocity of -8 m/s:
∆v = -8 m/s - 11 m/s = -19 m/s (since the object's velocity decreased)

Now we can calculate the impulse (∆p) using the same formula:

∆p = 27 kg * (-19 m/s) = -513 kg·m/s

Therefore, the impulse that acted on the object when it moved at -8 m/s after the collision is -513 kg·m/s.

To find the impulse that acted on the object, we need to use the impulse-momentum principle, which states that the impulse (J) is equal to the change in momentum (Δp) of the object.

The momentum of an object is calculated by multiplying its mass (m) by its velocity (v).

So, the initial momentum of the object before the collision is given by:

Initial momentum (p_initial) = mass (m) x initial velocity (v_initial)

The final momentum of the object after the collision is given by:

Final momentum (p_final) = mass (m) x final velocity (v_final)

Now, the change in momentum (Δp) is calculated by subtracting the initial momentum from the final momentum:

Δp = p_final - p_initial

Once we have the change in momentum, we can calculate the impulse (J) by using the formula:

J = Δp

Let's calculate the impulse for the given velocities:

a. For a final velocity of 8 m/s:
First, calculate the final momentum:
p_final = mass (m) x final velocity (v_final)

Using the given values:
p_final = 27 kg x 8 m/s

Now, calculate the change in momentum:
Δp = p_final - p_initial

Since the initial velocity is given as +11 m/s, the initial momentum is:
p_initial = mass (m) x initial velocity (v_initial)
p_initial = 27 kg x 11 m/s

Substitute the values into the change in momentum formula:
Δp = (27 kg x 8 m/s) - (27 kg x 11 m/s)

Once you calculate Δp, that will give you the impulse (J).

b. For a final velocity of -8 m/s:
Follow the same steps as in part (a), but this time, substitute the final velocity with -8 m/s.