Question

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?

Answer 1

Answer:

The tomato fell from 1027.2ft

Step-by-step explanation:

Parameters given:

Height from window = 450ft

Time taken to get from window to ground = 2 secs

V0, initial speed of tomato from drop point = 0 ft/s

Acceleration due to gravity = 32.2 ft/s^2

When the tomato gets to the observer at the window, its initial speed is no longer 0ft/s but an unknown value, u.

We can apply one of the equations of linear motion to then find this initial velocity at the window using the other parameters given i.e.  

s = ut + 1/2 at2^2

s = 450ft

t = 2 secs

a = g = 32.2ft/sec2^2

=> 450 = (u*2) + (1/2 * 32.2 * 2^2)

450 = 2u + 64.4

2u = 450 – 64.4

2u = 385.6

=> u = 192.8ft/s

Now that we know this initial velocity, we can use another equation of linear motion to find the height distance between the drop point and the window ,

v^2 - u^2 = 2gs

where s = distance between drop point and window

v = 192.8ft/s

u = 0ft/s;

=> 192.8^2 - 0^2 = 2*32.2*s

37171.84 = 64.4s

=> s = 37171.84/64.4

s = 577.20ft

Hence, distance from drop point to the ground, H, will be the addition of s and the height from the window to the ground:

=>H = 577.20 + 450

H = 1027.2ft

Answer 2

Answer:

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