Question

Q.an objects through vertically upwords reches a height of320m .
➡️what was its intial velocity? how long will the object taken to come back Earth?assumeg=10m/s2 .​

Answer 1

Let the initial velocity = u

final velocity = v

v= 0 m/s

s = 320 m

2gs = v²−u²

2 (-10)320= u²

u = 80m/s

v = u + at

0 = 80 - 10 t

t = 8 s

total time taken = 16sec.

Answer 2

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Given :-

An object through vertically upwards reaches a height of 320 m.

To Find :-

What is the initial velocity.

How long will the object taken to come back to the Earth.

Solution :-

First, we have to find the initial velocity :

As we know that :

• Newton third equation of motion :

$\begin{gathered} \longmapsto \rm\boxed{\bold{\red{{v}^{2} =\: {u}^{2} + 2as}}}\\\end{gathered}$

where,

v = Final Velocity

u = Initial Velocity

a = Acceleration

s = Distance travelled

Given :

Final velocity = 0 m/s

Distance travelled = 320 m

Acceleration = - 10 m/s²

According to the question by using the formula we get,

$\implies \sf {0}^{2} =\: {u}^{2} + 2 \times (- 10) \times 320 \\ \\ \implies \sf 0 =\: {u}^{2} - 20 \times 320 \\ \\ \implies \sf 0 =\: {u}^{2} - 6400 \\ \\ \implies \sf \cancel{-} {u}^{2} =\: \cancel{-} 6400 \\ \\ \implies \sf {u}^{2} =\: 6400 \\ \\ \implies \sf u =\: \sqrt{6400} \\ \\ \implies \rm\bold{\pink{u =\: 80\: m/s}}$

∴ The initial velocity is 80 m/s .

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Now, we have to find the how long will the object taken to come back to the Earth :

As we know that:

• Newton first law of motion :

$\begin{gathered} \longmapsto \sf\boxed{\bold{\red{v =\: u + at}}}\\\end{gathered}$

where,

v = Final Velocity

u = Initial Velocity

a = Acceleration

t = Time

Given :

Final Velocity = 0 m/s

Initial Velocity = 80 m/s

Acceleration = - 10 m/s²

According to the question by using the formula we get,

$\implies \sf 0 =\: 80 + (- 10) \times t \\ \\ \implies \sf 0 =\: 80 - 10t \\ \\ \implies \sf \cancel{-} 80 =\: \cancel{-} 10t \\ \\ \implies \sf 80 =\: 10t \\ \\ \implies \sf \dfrac{8\cancel{0}}{1\cancel{0}} =\: t \\ \\ \implies \sf \dfrac{8}{1} =\: t \\ \\ \implies \sf 8 =\: t \\ \\ \implies \rm\bold{\pink{t =\: 8\: seconds}}$

∴ The time taken to come back to the Earth is 8 seconds .