Question

A stone is dropped from a cliff. What will be its speed when it has fallen 100 m.

Answer 1

Answer:

The distance travelled by the stone = 100 m.

The acceleration due to gravity = 10 m/s.

Initial speed of the stone = 0 m/s.

We can find the final speed in two methods:

Method 1:

Using the second equation of motion:

⇒ s = ut + ½at²

⇒ 100 = 0×t + ½×10×t²

⇒ 100 = 0 + 5t²

⇒ 5t² = 100

⇒ t² = 100/5

⇒ t² = 20 s

⇒ t = 4.47 s

Hence, the time taken to reach the ground from cliff = 4.47 s.

Now, using the first equation of motion:

⇒ v = u + at

⇒ v = 0 + 10×4.47

⇒ v = 44.7 m/s

Hence, the speed when it falls = 44.7 m/s.

Method 2:

Using the third equation of motion:

⇒ v² - u² = 2as

⇒ v² - 0² = 2×10×100

⇒ v² = 20 × 100

⇒ v² = 2000

⇒ v = √2000

⇒ v = 44.7 m/s

Hence, the speed when it falls = 44.7 m/s.

Answer 2

Answer:

Initial speed = zero

We have to find speed of stone when it has fallen 100m..

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◈ For a body falling freely under the action of gravity, g is taken positive.

Third equation of kinematics :

v² - u² = 2gH

v denotes final speed

u denotes initial speed

g denotes acc. due to gravity

H denotes distance/height

➝ v² - 0² = 2(10)(100)

➝ v² = 2(1000)

➝ v = √2000

➝ v = 44.72 m/s