Question

A stone is dropped from the top of a 40 m high tower. Calculate its speed after 2 s. Also find the speed with which the stone strikes the ground.​

Answer 1

$\huge\bf{\underline{\underline{\sf{\red{Answer:}}}}}$

$\large\implies{\boxed{\sf{\blue{The\:speed\:of\:the\:stone\:after\:2s\:is\:19.6 m/s.}}}}$

$\large\implies{\boxed{\sf{\orange{The\:speed\:with\:which\:the\:stone\:strikes\:the\:ground\:is\:28\:m/s}}}}$

$\huge\bf{\underline{\underline{\sf{\purple{Explanation:}}}}}$

✤ Given :

Height = 40m

Time = 2 sec

✤ To Find :

It's speed after 2s.

The speed with which the stone strikes the ground.

✤ Solution :

Formulae used :

➤$\large{\boxed{\sf{\pink{v=u+at}}}}$

where, u = 0 and a = g(acceleration due to gravity)

Substituting the values, we get,

:$\Rightarrow{\sf{v = 0+9.8 \times 2}}$

:$\Rightarrow{\sf{v = 19.6m/s}}$

The speed of the stone after 2s is 19.6 m/s.

After that, we have to find the stone strikes the ground,

Fomulae used :

➤$\large{\boxed{\sf{\pink{v^{2}=u^{2}+2gs}}}}$

Substituting the values, we get,

:$\Rightarrow\displaystyle{\sf{v^{2} = 0+2 \times 9.8 \times 40}}$

:$\Rightarrow\displaystyle{\sf{v^{2}=784}}$

:$\Rightarrow\displaystyle{\sf{v^{2}=784}}$

:$\Rightarrow\displaystyle{\sf{v=\sqrt{784}}}$

:$\Rightarrow\displaystyle{\sf{v=28m/s}}$

Therefore, the speed with which the stone strikes the ground is 28m/s.

__________________________

Answer 2

Given:

Height= 40m

Time= 2seconds

To find:

Speed of stone after 2 seconds and speed of the stone with which strikes the ground.

Solution:

To find the stone after 2 seconds we will use the formula,

$v=u+at$

where,

$v$ is the final velocity

$u$ is the initial velocity which is 0

$a$ is the acceleration due to gravity which is $9.8 m/s$

$t$ is the time taken which is 2seconds

Putting the values,

$v=0+9.8$×$2$

⇒$v=19.6m/s$

To find the speed with which the stone will strike the stone, we will use the formula,

$v^2=u^2-2aS$

where,

$S$ is the height

Putting the values, we get,

$v^2=0+2$×$9.8$×$40$

⇒$v^2=784$

Taking square root from both sides, we get,

⇒$v=\sqrt{784}$

⇒$v=28m/s$

Hence, the speed of stone after 2seconds is $19.6m/s$ and the speed with which it will strike the ground is $28m/s$.