Question

A stone is dropped from a height of 500m. Calculate the time taken by it to fall and the velocity with which it hits the ground. (G=10m/s2)

Answer 1

Given data :

A stone is dropped from a height of 500 m.

Acceleration due to gravity g = 10 m/s²

To find :

1) Time taken by the stone to fall on the ground.

2) Velocity with which the stone hits the ground.

Solution :

As the stone is 'dropped', its initial velocity u = 0 m/s

1) Calculating the time taken by the stone to fall on the ground :

Distance S = 500 m

Acceleration due to gravity g = 10 m/s²

Initial velocity u = 0 m/s

Time t = ? s

The relation between the elements taken is :

S = ut + $\frac{1}{2}$ gt²

⇒ 500 = (0)(t) + $\frac{1}{2}$ (10)(t²)

⇒ 500 = 0 + 5t²

⇒ 5t² = 500

⇒ t² = 100

⇒ t = √100

⇒ t = 10 seconds

Therefore, The stone takes 10 seconds to hit the ground.

2) Calculating the velocity with which the stone hits the ground :

Acceleration due to gravity g = 10 m/s²

Initial velocity u = 0 m/s

Final velocity v = ? m/s

Time taken t = 10 s

The relation between the elements taken is :

v = u + gt

⇒ v = 0 + (10)(10)

⇒ v = 100 m/s

Therefore, The stone hits the ground with the velocity of 100 m/s.

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