Final answer:
Using the provided kinematic equation and given parameters, the final velocity of the rock after 1 second is found to be -16.4 m/s, indicating that it is moving downwards.
Step-by-step explanation:
The velocity of the rock after 1 second can be determined by using the kinematic equations which consider the initial velocity, acceleration due to gravity, and the displacement of the rock. Given that the initial velocity (vo) is -13.0 m/s, the acceleration (a) is -9.8 m/s² (due to gravity), and the displacement from the starting point (y1) is -5.10 m, we can use the equation v² = vo² + 2a(y - yo) to find the final velocity v at the given time.
To solve for the velocity v at time t=1 s, we calculate
- v² = (−13.0 m/s)² + 2(−9.80 m/s² ) (−5.10 m – 0 m)
- v² = 268.96 m²/s²
- v = ±√268.96 m²/s² = ±16.4 m/s
Considering the direction of the velocity, we choose the negative root to indicate that the rock is heading downwards, thus v = -16.4 m/s.