Given:
- Speed of the rod, v = 0.8c (where c is the speed of light)
- Angle between the direction of motion and the length of the rod, θ = 60°

To find:
The percentage contraction in the length of the rod.

Explanation:

1. Length Contraction:
According to the theory of Special Relativity, objects moving at relativistic speeds undergo length contraction. The length of an object in its rest frame is called its proper length, and when the object is moving relative to an observer, its length appears shorter in the direction of motion. This phenomenon is known as length contraction.

2. Formula for Length Contraction:
The formula to calculate the length contraction is given by:
L' = L√(1 - v^2/c^2)
where,
L' is the contracted length of the rod,
L is the proper length of the rod,
v is the velocity of the rod, and
c is the speed of light.

3. Calculation:
Given that the rod is moving with a speed of 0.8c, we have:
v = 0.8c

The angle between the direction of motion and the length of the rod is 60°. Since the length contraction occurs along the direction of motion, we need to consider the component of velocity along the length of the rod.

The component of velocity along the length of the rod can be calculated using trigonometry:
v_parallel = v * cos(θ)
= 0.8c * cos(60°)
= 0.8c * 0.5
= 0.4c

Substituting the values in the length contraction equation:
L' = L√(1 - (0.4c)^2/c^2)
L' = L√(1 - 0.16)
L' = L√(0.84)
L' = 0.917L

4. Percentage Contraction:
The percentage contraction in the length of the rod can be calculated using the formula:
Percentage Contraction = (L - L')/L * 100

Substituting the values:
Percentage Contraction = (L - 0.917L)/L * 100
Percentage Contraction = (0.083L)/L * 100
Percentage Contraction = 8.3%

Hence, the percentage contraction in the length of the rod is 8.3%.