Respuesta :
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:
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
