Question

Two stone A and B are dropped from the top of two different towers such that they travel 44.1 m and 63.7m in the last second of their motion , respectively. Find the ratio of the height of two towers from where the stone are dropped

Answer 1

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Answer 2

Answer:

The ratio of the height of two towers from where the stone are dropped is 17:31.

Explanation:

Given that,

First stone covers distance = 44.1 m  in last second

Second stone covers distance = 63.7 m in last second

For the velocity of first stone,

Using equation of motion

$s=ut-\dfrac{1}{2}gt^2$

$44.1=u-\dfrac{1}{2}\times9.8\times1$

$u = 44.1+4.9=49\ m/s$

For the velocity of second stone,

Using equation of motion

$s'=u't-\dfrac{1}{2}gt^2$

$63.7=u'-\dfrac{1}{2}\times9.8\times1$

$u' = 63.7+4.9=68.6\ m/s$

Now, the distance of first stone after dropped

Using equation of motion again

$v^2-u^2=2as$

$(49)^2=2\times9.8\times s_{1}$

$s_{1} = \dfrac{49\times49}{2\times9.8}$

$s_{1}=122.5\ m$

$s_{1}=122.5+44.1=166.6\ m$

Now, the distance of second stone after dropped

$(68.6)^2=2\times9.8\times s_{2}$

$s_{2}=\dfrac{68.6\times68.6}{2\times9.8}$

$s_{2}=240.1\ m$

$s_{2}=240.1+63.7=303.8\ m$

The ratio of the height of two towers is

$\dfrac{s_{1}}{s_{2}}=\dfrac{166.6}{303.8}$

$\dfrac{s_{1}}{s_{2}}=\dfrac{17}{31}$

Hence, The ratio of the height of two towers from where the stone are dropped is 17:31.