Question

(Another tomato/skyscraper problem.) 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 v0 = 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? Give your answer as a decimal approximation with units.

Answer 1

A tomato dropped and takes 2 seconds to hit the ground from a window 450 feet high is initially dropped from a height of approximately 156.76 meters above the ground.

Step-by-step explanation:

To calculate the height from which the tomato was dropped, we can use the kinematic equations for free fall motion. Since the tomato is dropped, its initial velocity is 0 m/s. We also know that the acceleration due to gravity (g) is approximately 9.8 m/s².

Let's use the following kinematic equation:

s = ut + ½t²

Here, s is the displacement, u is the initial velocity (0 m/s), and t is the time.

When the tomato has fallen for 2 seconds from your window (450 feet above the ground), we calculate the distance it falls in that time frame:

s = 0² + ½(9.8 m/s²)(2 s)²

s = 0 + 19.6 m

s = 19.6 m (64.304 feet)

We need to convert the window height to meters:

450 feet * 0.3048 m/foot = 137.16 meters

Now, we add this distance to the 19.6 meters that the tomato fell to find the total fall distance.

Total drop height = Window height + Distance fallen

Total drop height = 137.16 m + 19.6 m

Total drop height = 156.76 m

The height from which the tomato was dropped is approximately 156.76 meters (or as a decimal approximation in feet: 514.304 feet).

Answer 2

1027.2 m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 32.2 ft/s

`s=ut+(1)/(2)at^2\\\Rightarrow u=(s-(1)/(2)at^2)/(t)\\\Rightarrow u=(450-(1)/(2)* 32.2* 2^2)/(2)\\\Rightarrow u=192.8\ ft/s`

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(192.8^2-0^2)/(2* 32.2)\\\Rightarrow s=577.20\ m`

The height the tomato would fall is 450+577.2 = 1027.2 m