Final answer:
The speed of the penny when it hits the ground after being dropped from a height of 778 meters is approximately 123.5 meters per second.
Step-by-step explanation:
To calculate the speed of the penny when it hits the ground after being dropped from a height of 778 meters, we can use the equations of motion for an object in free fall under the influence of gravity (ignoring air resistance). The equation that relates initial velocity (vi), acceleration due to gravity (g), and the height (h) from which the object is dropped to the final velocity (vf) is given by:
vf2 = vi2 + 2gh
Since the penny is dropped, its initial velocity is 0 m/s, and the acceleration due to gravity is approximately 9.81 m/s2. Plugging these values into the equation, we can solve for the final velocity:
vf2 = 0 + 2(9.81 m/s2)(778 m)
vf = √(2 * 9.81 m/s2 * 778 m)
vf ≈ √(15253.16 m2/s2)
vf ≈ 123.5 m/s (rounded to the nearest tenth)
The penny would hit the ground with a final velocity of approximately 123.5 meters per second.