Final answer:
The rock falls 93.67 meters after 4.2 seconds when thrown downward off a cliff at an initial speed of 1.7 m/s. This calculation uses the kinematic equation accounting for initial velocity and acceleration due to gravity. None of the provided options match this result.
Step-by-step explanation:
The student is asking about the distance a rock will fall after being thrown downward off a cliff with a given initial speed and time elapsed. To solve this, we use the kinematic equation for distance under constant acceleration, which is gravity. The formula is:
d = v_i * t + ½ * a * t^2
Where:
- d is the distance fallen
- v_i is the initial velocity (1.7 m/s downward)
- t is the time elapsed (4.2 seconds)
- a is the acceleration due to gravity (9.8 m/s^2 downward)
Plugging in the values:
d = 1.7 m/s * 4.2 s + ½ * 9.8 m/s^2 * (4.2 s)^2
d = 7.14 m + ½ * 9.8 m/s^2 * 17.64 s^2
d = 7.14 m + 86.53 m
d = 93.67 m
However, as per the given options, none matches the calculated result, indicating that there might be a mistake in either the provided options or the calculation. Given the provided values and the correct application of physical laws, the rock would fall 93.67 meters after 4.2 seconds. Therefore, we need to verify the values or the options given in the problem.