A baseball player hits a home run over the left-field fence, which is 104 m from home plate. The ball is hit at a point 1.08 m directly above home plate, with an initial velocity directed 35.0° above the horizontal. By what distance does the baseball clear the 3.00 m high fence, if it passes over it 2.80 s after being hit?

To find the distance the baseball clears the fence, we first need to determine the vertical and horizontal components of its initial velocity.

Given:
- The initial velocity is directed 35.0° above the horizontal.
- The magnitude of the initial velocity is not given.

We can use the following trigonometric formulas to calculate the horizontal and vertical components of the initial velocity:

Horizontal component (Vx) = initial velocity * cos(angle)
Vertical component (Vy) = initial velocity * sin(angle)

Let's substitute the given information into these formulas.

Vx = initial velocity * cos(35.0°)
Vy = initial velocity * sin(35.0°)

The baseball's path can be divided into two parts: the horizontal motion and the vertical motion. We can analyze these two motions separately.

For the horizontal motion:
- The horizontal velocity (Vx) remains constant throughout the motion.
- The distance (dx) covered is given by the formula dx = Vx * t

For the vertical motion:
- The vertical velocity (Vy) changes due to the acceleration due to gravity.
- The initial vertical velocity at t = 0 is Vy.
- The final vertical velocity (Vf) at t = 2.80 s can be calculated using the equation Vf = Vy + (g * t), where g is acceleration due to gravity (9.8 m/s^2).
- The vertical displacement (dy) covered is given by the formula dy = Vy * t + (1/2) * g * t^2

Now, let's calculate the horizontal distance covered by the baseball.

dx = Vx * t
= (initial velocity * cos(35.0°)) * 2.80 s

To find the vertical displacement, we need to calculate both Vy and dy.

Vy = initial velocity * sin(35.0°)
dy = Vy * t + (1/2) * g * t^2
= (initial velocity * sin(35.0°)) * 2.80 s + (1/2) * (9.8 m/s^2) * (2.80 s)^2

The total distance covered by the baseball is the diagonal distance from home plate to the point where it clears the fence. This distance can be calculated using the Pythagorean theorem, considering the horizontal and vertical components of displacement:

Total distance = sqrt(dx^2 + dy^2)

Now, we have all the necessary formulas to find the distance the baseball clears the fence. We just need the value of the initial velocity. Unfortunately, the magnitude of the initial velocity is not given in the question. If you provide the magnitude of the initial velocity, I can help you calculate the distance the baseball clears the fence.