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  • A stone is allowed to fall from the top of the tower 100m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/ calculate when and where 2 stones will meet.

A stone is allowed to fall from the top of the tower 100m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet

Answers (1)

best_answer

 Given, 

Height (h) = 100 m.

According to the question,

Let the two stones meet after t seconds at a point P which is at a height x above the ground as shown in figure.

 

 

For stone 1,

$
\begin{aligned}
& \mathrm{u}=0, \mathrm{~h}=(100-\mathrm{x}) \mathrm{m}, \\
& a=g=9.8 \mathrm{~m} / \mathrm{s}^2
\end{aligned}
$


From s $=\mathrm{ut}+\frac{1}{2} \mathrm{gt}^2$

$
(100-x)=0+\frac{1}{2} \times 9.8 t^2=4.9 t^2
$


For stone 2,

$
u=25 m / s, h=x, a=g=-9.8 m / s^2
$


Froms $=\mathrm{ut}+\frac{1}{2} \mathrm{at}^2$

$
x=25 t+\frac{1}{2}(-9.8) t^2=25 t-4.9 t^2
$


Adding equations (i) and (ii)

$
100-x+x=25 t \Rightarrow t=\frac{100}{25}=4 s
$


From equation (i),

$
\begin{aligned}
& 100-x=4.9 \times(4)^2=78.4 \\
& x=100-78.4=21.6 \mathrm{~m}
\end{aligned}
$
 

Posted by

Ritika Jonwal

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