A ball, initially at rest, falls freely from the top of a building and reaches a maximum velocity of 40 m/s. Find the height of the building. (Use acceleration due to gravity, g =10 m/s²)

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RRB ALP Electrician 22 Jan 2019 Official Paper (Shift 3)

Answer 1

Concept:

Equation of motion:

Equations of motion of kinematics describe the basic concept of the motion of an object such as the position, velocity, or acceleration of an object at various times.
These three equations of motion govern the motion of an object in 1D, 2D, and 3D.
Three equations:
1. v = u + at
2. s = ut + 0.5 at²
3. 2as = v² - u²
Here, u = initial velocity, v = final velocity, s = displacement, t = time
Under the influence of gravity, acceleration a is replaced by acceleration due to gravity g.

Calculation:

Given,

Initial velocity, u = 0m/s, Final velocity, v = 40 m/s, Acceleration due to gravity, g = 10 m/s²

From the third equation of motion under the influence of gravity,

2gh = v² - u²

\(\Rightarrow h=\frac{v^2-u^2}{2g}\)

\(\Rightarrow h=\frac{40^2-0^2}{2\times 10}=80~m\)

Hence, the maximum height is 80 m.

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