Question

From the top of a tower of height 78.4 m two stones are projected horizontally with 10 m/s and 20 m/s in opposite directions. On reaching the ground, their separation is 60n then n = ________

Answer 1

$\mathcal{\huge{\fbox{\red{Question:-}}}}$

✴ From the top of a tower of height 78.4 m two stones are projected horizontally with 10 m/s and 20 m/s in opposite directions. On reaching the ground, their separation is 60n then n = ________

$\mathcal{\huge{\fbox{\green{AnSwEr:-}}}}$

➡ On reaching the ground, their separation is 60n then n = 120m.

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

Given :-

• The Height of tower (h) =78.4 m
• Speed of first stone(u) = 10 m/s
• Speed of second stone(v) = 20 m/s

To Find :-

• The value of n.

Calculation :-

According to the question,

◼ First, x1 = u × t1

➡ x1 = 10 m/s × t1

Where, t1 = √ 2.h / g

➡ x1 = 10 m/s x √ 2.h / g

➡ x1 = 10 √ 2.h / g .......... (1)

◼ Again, x2 = u × t2

➡ x2 = 20 x c

Where, t2 = √ 2.h / g

➡ x2 = 20 √ 2.h / g .......... (2)

✨ Adding equation 1 & 2

We get (x1 + x2) , works as separating stones.

↗ 10 √ 2.h / g + 20 √ 2.h / g

↗ 30 √ 2.h / g

↗ 30 x √ 2 x 78.4 / 10

↗ 30 x √ 156.8 / 9.8

↗ 30 x √ 16

➡ 30 x 4 = 120 m

➡ Thus the separation between the stones is 120 m.

_____________________________________

Answer 2

n = 2  , On reaching the ground, their separation is  120 m

Explanation:

Tower height = 78.4 m

S = ut + (1/2)at²

Vertical initial speed is zero

=> 78.4 =  (1/2)(9.8)t²

=> t² = 16

=> t = 4

Horizontal Distance by 10 m/s  = 10 * 4 = 40 m

Horizontal Distance by 20 m/s  = 20 * 4 = 80 m

Distance of separation = 40 + 80 = 120 m

120 = 60 * 2 m

Comparing with 60 n

n = 2

On reaching the ground, their separation is  120 m

n = 2

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