You are looking out your window in a skyscraper, and again your window is at a height of 450 feet above the ground. This time, however, you know that the tomato was dropped (so v_0 = 0), but you did not see it dropped so you do not know when it was dropped. You measure that it takes exactly 2 seconds from the time the tomato passes your window until it hits the ground. From what height did it fall?

1027.2 m

Step-by-step explanation:

Given:

- V_o = 0 m/s

- s (t_1) = 450 ft

- t_f - t_1 = 2 s ... 1

- s (0) = 0

- g = 32.2 ft/s^2

Find:

Height of the skyscraper h

Solution:

- Find the height h in terms of t_1:

s (t_1) = s (0) + v_o*t_1 + 0.5*g*t_1^2

h - 450 = 0 + 0 + g*t_1^2 / 2

h = g*t_1^2 / 2 + 450 ... 2

- Find the height h in terms of t_f:

s (t_f) = s (0) + v_o*t_f + 0.5*g*t_f^2

h = 0.5*g*t_f^2 ... 3

- Equate Equations 2 and 3 and then substitute Equation 1:

0.5*g*t_f^2 = g*t_1^2 / 2 + 450

substitute: 0.5*g*t_f^2 = (g * (t_f - 2) ^2) / 2 + 450

(g*t_f^2 / 2) - 2*g*t_f + 2g + 450 = (g*t_f^2 / 2)

-2*g*t_f + 2g = - 454

t_f = (454 / 2*g) + 1 = 7.9876 s

- Back substitute t_f in Equation 3:

h = 0.5*g * (t_f) ^2

h = 0.5*32.2*7.9876^2

h = 1027.2 m