Question

A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m/s with what velocity will it strike the ground?​

Answer 1

Answer:

20 m/s

Explanation:

As per the provided information in the given question, we have :

• Intial velocity (u) = 0 m/s

[When the body is thrown vertically downwards, its initial velocity is taken as 0.]

• Height (h) = 20 m
• Acceleration (a) = +10 m/s²

[ As the body is thrown in downward direction from a height, so its acceleration will be positive.]

We are asked to calculate the velocity with which it'll strike the ground or final velocity (v).

Here, we'll be using the third equation of motion for frèély falling bodies.

$\\ \longrightarrow \quad \pmb{\boxed{\sf {v^2 - u^2 = 2gh}} }$

• v denotes final velocity
• u denotes initial velocity
• g denotes acceleration due to gravity
• h denotes height

Substituting the values we have,

$\\ \longrightarrow \sf{\quad { v^2 - (0)^2 = 2 \times 10 \times 20 }}$

$\\ \longrightarrow \sf{\quad { v^2 = 400 }}$

$\\ \longrightarrow \sf{\quad { v = \sqrt{400} }}$

$\\ \longrightarrow \sf{\quad { v = 20 }}$

$\\ \longrightarrow \bf{\quad\underline { Final \; velocity = 20 \; m/s }}$

Therefore, with 20 m/s of velocity , it'll strike the ground.

Some more information :

Equations of motion for frèély falling bodies :

$\boxed{ \begin{array}{cc} \pmb{\sf{ \quad \: v = u + gt \quad}} \\ \\ \pmb{\sf{ \quad \: h= ut + \cfrac{1}{2}g{t}^{2} \quad \: } } \\ \\ \pmb{\sf{ \quad \: {v}^{2} - {u}^{2} = 2gh \quad \:}}\end{array}}$

• v denotes final velocity
• u denotes initial velocity
• g denotes acceleration due to gravity
• t denotes time
• h denotes height

Answer 2

Answer:

Given :-

A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m/s²

To Find :-

Velocity when it strikes ground or the final Velocity

Solution :-

As it starts from rest so

Initial velocity = 0 m/s

Height = 20 m

Acceleration due to gravity = 10 m/s²

We know that

v² = u² + 2gh

v² = (0)² + 2(10)(20)

v² = 0 + 2(10)(20)

v² = 0 + 400

v² = 400

v = √(400)

v = 20

Therefore,

Final Velocity is 20 m/s