Final answer:
Calculating the distance a rock falls involves using the kinematic equation d = v_i * t + (1/2) * a * t^2. For a rock thrown downward at 1.7 m/s from a cliff, after 4.2 seconds, the calculated distance is 93.3 meters, which does not match any of the given options.
Step-by-step explanation:
The question pertains to the calculation of the distance a rock falls when thrown off a cliff with an initial downward velocity. To find the distance fallen after a certain time when the rock is thrown downward, we can use the kinematic equation for uniformly accelerated motion:
d = v_i * t + (1/2) * a * t^2
Where:
- d represents 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)
By substituting in the given values:
d = 1.7 * 4.2 + (1/2) * 9.8 * 4.2^2
d = 7.14 + (1/2) * 9.8 * 17.64
d = 7.14 + 86.1624
d = 93.3024 meters
However, none of the given options (a) 35.3 meters, (b) 17.7 meters, (c) 76.9 meters, (d) 7.77 meters matches the calculated distance. It appears there has been a miscalculation or the given options are incorrect. The correct answer should be 93.3 meters, provided that air resistance is ignored and the acceleration due to gravity is 9.8 m/s^2.