Final answer:
The formula for the displacement and velocity of a rock thrown straight down from the Verrazano Narrows Bridge can be determined using the equations of motion. The initial velocity of the rock is 14.0 m/s, and the height of the bridge above the water is 70.0 m. Assuming negligible air resistance, you can use the displacement formula to calculate the rock's position at different times.
Step-by-step explanation:
The formula for the displacement and velocity of a rock thrown straight down from the Verrazano Narrows Bridge can be determined using the equations of motion. The initial velocity of the rock is 14.0 m/s, and the height of the bridge above the water is 70.0 m. Assuming negligible air resistance, we can use the equation:
displacement = initial velocity * time + (1/2) * acceleration * time^2
where the acceleration is due to gravity, which is approximately 9.8 m/s^2. We can substitute the values of time (a) into this equation to calculate the displacement and velocity at different times. For example, when a = 0.500 s, the displacement would be:
displacement = 14.0 m/s * 0.500 s + (1/2) * 9.8 m/s^2 * (0.500 s)^2
And the velocity would be:
velocity = initial velocity + acceleration * time
Using these formulas, you can calculate the displacement and velocity at the given times.