**Solution:**

To solve this problem, we need to analyze the projectile motion of the body and calculate the change in momentum when it strikes the ground.

**Projectile Motion Analysis:**

When a body is projected at an angle of 45 degrees with the horizontal, it can be resolved into two components: one along the horizontal direction and the other along the vertical direction.

- The horizontal component of velocity (u) remains constant throughout the motion.
- The vertical component of velocity (v) can be calculated using the equation v = u * sin(θ), where θ is the angle of projection.

**Time of Flight:**

The time taken by the body to reach the ground can be calculated using the equation:

t = 2 * u * sin(θ) / g

where g is the acceleration due to gravity.

**Maximum Height:**

The maximum height reached by the body can be calculated using the equation:

H = (u^2 * sin^2(θ)) / (2 * g)

**Change in Momentum:**

The change in momentum is given by the equation:

Δp = m * (v - u)

where m is the mass of the body, v is the final velocity, and u is the initial velocity.

Since air resistance is negligible, the final velocity of the body just before it strikes the ground is equal to the initial velocity in the vertical direction (v = u * sin(θ)).

Substituting the values in the equation for change in momentum:

Δp = m * (u * sin(θ) - u)

Δp = m * u * (sin(θ) - 1)

Δp = m * u * (sin(45°) - 1)

Δp = m * u * (1/√2 - 1)

Simplifying,

Δp = m * u * (√2 - 1)

Therefore, the total change in momentum when the body strikes the ground is **(√2 - 1) times mu**, which corresponds to option 3) mu.