Question

A ball is dropped from a height 50 m. If it reaches the ground. Then calculate the distance and displacement covered by the ball.

with explanation please ​

Answer 1

Answer:

Total distance D = 50 +(0.5*50*2)

+0.5(0.5*50*2) +0.5*0.5(0.5*50*2) + …

Let x = (0.5*50*2) = 50

And rewrite total distance

D = 100 + 0.5^1*x +0.5^2*x +0.5^3*x + ...

= 100 + 50[0.5^1 +0.5^2 +0.5^3 + ...]

= 100 +50[Σ 0.5^n, n=1 to inf]

The sum in square brackets is

1/2 + 1/4 + 1/8 + 1/16 …

which can be evaluated in a spreadsheet, computer program or online math tool, but familiarity with binary numbers makes it easy. The sum expression in binary is:

0.1 + 0.01 + 0.001 + 0.0001 …

which adds to a fraction filled with 1s

0.1111 …

whose limit is a tiny bit less than 1.

Therefore,

D 100 +50[1] = 150 m.