Aperson flings a nickel off of the willis tower (h = 324 m) with a downward velocity of magnitude v0 = 6 m/s. a. calculate the time t, in seconds, that it takes for the nickel to fall.
b. find the speed at which the nickel strikes the ground vf, in meters per second, using the initial velocity, v0, and the drop distance, h.

a) It takes 7.5 s for the nickel to fall.

b) The speed will be 79.5 m/s

Explanation:

The equations for the height and velocity of the nickel at time "t" are the following:

y = y0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

y = height of the nickel at time t

y0 = initial height

v0 = initial velocity

t = time

g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive)

v = velocity at time t

a) When the nickel hits the ground its height is 0. Then, using the equation for height, we can calculate the time it takes the nickel to fall.

y = y0 + v0 · t + 1/2 · g · t²

0 = 324 m - 6 m/s · t - 1/2 · 9.8 m/s² · t²

0 = -4.9 m/s² · t² -  6 m/s · t + 324 m

Solving the quadratic equation:

t = 7.5 s

It takes 7.5 s for the nickel to fall.

b) The speed at which the nickel hits the ground will be the speed after 9 s of falling. Then, using the equation of velocity:

v = v0 + g · t

v = -6 m/s - 9.8 m/s² · 7.5 s

v = -79.5 m/s

The speed will be 79.5 m/s

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