Question

Find separation between A and B after 3 sec is 2 balls with initial speed 0 and 3m/s respectively are thrown from a building.

Expanation needed ​

Answer 1

The separation between the ball A and B is 9 m.

Given -:

time = 3s

Initial speed ( ball A )= 0 m/s

initial speed ( ball B ) = 3 m/s

To Find -:

The separation between the thrown balls after 3 s

Formula used -:

${\bf {\underline{s \: = ut + \frac{1}{2} g {t}^{2} }}}$

U = initial speed

t = time

g = Acceleration due to gravity ( 9.8 = 10 m/s²)

Solution :

Substitute the values in equation ,

For finding the ball (A) :

$\begin{gathered}\sf\implies \: s = u_{1} t+ \frac{1}{2} \: g {t}^{2} \\ \\ \implies\sf \: 0 \times 3 + \frac{1}{2} \times 10 \times {3}^{2} \\ \\ \sf\implies \: 0 + \frac{1}{2} \times 10 \times 9 \\ \\ \sf\implies \: 5 \times 9 \\ \\ \bf \implies 45\end{gathered}$

ie, S1 = 45 m

For Ball ( B ) :

$\begin{gathered}\sf\implies \: s = u_{2} \: t \: + \frac{1}{2} \: g \: {t}^{2} \\ \\ \sf\implies \: 3 \times 3 + \frac{1}{2} \times 10 \times {3}^{2} \\ \\ \sf\implies \: 9 + \frac{1}{2} \times 10 \times 9 \\ \\ \sf\implies \: 9 + 5 \times 9 \\ \\ \bf\implies \: 54\end{gathered}$

ie, S2 = 54 m

Then, To find the separation between them = S2 - S1

$\begin{gathered}\bullet \: \: \sf s_{1} \: = 45 \\ \sf\bullet \: \: s_{2} \: = 54\\ \\ \sf \: s_{2} - s_{1} \: = 54 - 45 \\ \sf \: = 9 \: m\end{gathered}$

_______________________

Answer 2

Answer:

Solution :

Substitute the values in equation ,

For finding the ball (A) :

\begin{gathered}\begin{gathered}\sf\implies \: s = u_{1} t+ \frac{1}{2} \: g {t}^{2} \\ \\ \implies\sf \: 0 \times 3 + \frac{1}{2} \times 10 \times {3}^{2} \\ \\ \sf\implies \: 0 + \frac{1}{2} \times 10 \times 9 \\ \\ \sf\implies \: 5 \times 9 \\ \\ \bf \implies 45\end{gathered} \end{gathered}

⟹s=u

1

t+

2

1

gt

2

⟹0×3+

2

1

×10×3

2

⟹0+

2

1

×10×9

⟹5×9

⟹45

ie, S1 = 45 m

For Ball ( B ) :

\begin{gathered}\begin{gathered}\sf\implies \: s = u_{2} \: t \: + \frac{1}{2} \: g \: {t}^{2} \\ \\ \sf\implies \: 3 \times 3 + \frac{1}{2} \times 10 \times {3}^{2} \\ \\ \sf\implies \: 9 + \frac{1}{2} \times 10 \times 9 \\ \\ \sf\implies \: 9 + 5 \times 9 \\ \\ \bf\implies \: 54\end{gathered} \end{gathered}

⟹s=u

2

t+

2

1

gt

2

⟹3×3+

2

1

×10×3

2

⟹9+

2

1

×10×9

⟹9+5×9

⟹54

ie, S2 = 54 m

Then, To find the separation between them = S2 - S1

\begin{gathered}\begin{gathered}\bullet \: \: \sf s_{1} \: = 45 \\ \sf\bullet \: \: s_{2} \: = 54\\ \\ \sf \: s_{2} - s_{1} \: = 54 - 45 \\ \sf \: = 9 \: m\end{gathered} \end{gathered}

∙s

1

=45

∙s

2

=54

s

2

−s

1

=54−45

=9m