If the angle creates with the surface, then the answer must be option 4 (e=v2-v1/u1-u2 =v2-usintheta/usintheta v2=u(e+1)sintheta so,magnitude of impulse will be mu(1+e)sintheta) hope, it will help you

Impulse imparted to the surface by the ball

The impulse imparted to the surface by the ball can be determined by considering the change in momentum of the ball during the collision. The impulse is defined as the change in momentum, which can be calculated using the equation:

Impulse = Change in momentum

Change in momentum of the ball

The change in momentum of the ball can be calculated by subtracting the initial momentum from the final momentum. The initial momentum of the ball can be expressed as:

Initial momentum = mass of the ball * initial velocity

Since the ball is moving with a speed u and collides with the surface at an angle theta, the initial velocity can be expressed as:

Initial velocity = u * cos(theta)

Therefore, the initial momentum can be calculated as:

Initial momentum = m * u * cos(theta)

The final momentum of the ball can be expressed as:

Final momentum = mass of the ball * final velocity

Since the ball collides with a smooth horizontal surface, the vertical component of velocity is reversed while the horizontal component remains the same. The final velocity can be expressed as:

Final velocity = -u * sin(theta)

Therefore, the final momentum can be calculated as:

Final momentum = m * (-u * sin(theta))

Calculating the impulse

Now that we have the initial momentum and the final momentum, we can calculate the change in momentum and determine the impulse imparted to the surface by the ball.

Change in momentum = Final momentum - Initial momentum

Substituting the expressions for initial and final momentum:

Change in momentum = m * (-u * sin(theta)) - m * u * cos(theta)

Simplifying the expression:

Change in momentum = -m * u * sin(theta) - m * u * cos(theta)

Factorizing -m * u out of the expression:

Change in momentum = -m * u * (sin(theta) + cos(theta))

Since impulse is defined as the change in momentum, the impulse imparted to the surface by the ball is:

Impulse = -m * u * (sin(theta) + cos(theta))

However, the question asks for the magnitude of the impulse. Therefore, taking the magnitude:

|Impulse| = m * u * (sin(theta) + cos(theta))

Simplifying further:

|Impulse| = m * u * sqrt(2) * sin(theta + pi/4)

Comparing this expression with the given options, we can see that the correct answer is 4) mu(1 - e) * sin(theta).