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Estimate (a) how long it took King Kong to fall straight down from the top of the Empire State Building (380 m high), and (b) his velocity just before 鈥渓anding.鈥

Short Answer

Expert verified

(a) It will take 8.81 s to fall straight down from the top of the Empire State Building.

(b) The velocity of King Kong just before landing will be 86.34ms-1.

Step by step solution

01

Step1. Concept of free fall

When an object is falling only under the influence of gravity, the situation is called free fall. The acceleration of a body under free fall is9.8ms-2.

02

Step2. Given data and assumption

The height of the building,h=380m

The initial velocity of King Kong,u=0ms-1

Assume that the time taken to fall is t, the velocity just before landing is v, and acceleration due to gravity is g=9.8ms-2.

03

Step3. Using the second equation of motion

From the second equation of motion, you can write the displacement of King Kong as.

h=ut+12gt2

Substituting the values in the above equation, you get.

380=0+129.8t2

Solving the above equation fort, you get.

t=8.81s

Thus, the time taken by King Kong to fall from the building is 8.81 s.

04

Step4. Using the first equation of motion

From the first equation of motion, you can write the velocity of King Kong at any time t as.

v=u+gt

The velocity just before landing will be the velocity at time t.

Thus,

v=0+9.88.81=86.34ms-1

Thus, the velocity of King Kong just before landing will be 86.34ms-1.

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