Final answer:
The time it takes for the rock to complete 5.5 orbits, with a circular path of radius 4.6 m and a velocity of 4 m/s, is approximately 39.7375 seconds.
Step-by-step explanation:
To calculate the time it takes for the rock to make exactly 5.5 orbits, we first need to find the circumference of the circle the rock moves in, which is the distance covered in one complete orbit. The formula to calculate the circumference (C) is C = 2πr, where r is the radius.
For a radius of 4.6 m, the circumference of the circle is C = 2π(4.6 m) ≈ 28.9 m. Knowing the rock moves at a velocity (v) of 4 m/s, the time (t) to complete one orbit is t = C/v = 28.9 m / 4 m/s ≈ 7.225 s.
Therefore, the time to complete 5.5 orbits is t(total) = 5.5 × 7.225 s ≈ 39.7375 s.