Question

A stone is allowed to fall from the top of a tower 100 m 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.

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Answer 1

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• A stone is allowed to fall from the top of a tower 100 m 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.

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Here, height of the tower is 100 m. Now, suppose the two stones meet at a point which above the ground as shown in the figure, so that the distance of point P from the top of the lower is 100-x.

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★ For the stone falling from top of tower:

• Height, h = (100 - x) m
• Initial velocity, u = 0
• Time, t = ?
• Acceleration due to gravity, g = 9.8 m/s²

Now,

$\red{ \sf \: h = ut + \frac{1}{2} g {t}^{2} }$

$\sf \longrightarrow 100 - x = 0 \times t + \frac{1}{2} \times 9.8 \times {t}^{2}$

$\sf \longrightarrow 100 - x = 4.9 \: {t}^{2} \: \: \: \: \: - - - - (i)$

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★ For stone projected vertically upwards:

• Height,h = x m
• Initial velocity, u = 25 m/s
• Time, t = ?
• Acceleration due to gravity, g = - 9.8 m/s²

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$\red{ \sf s = ut + \frac{1}{2} g {t}^{2} }$

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

$\sf \longrightarrow x = 25 \: t - 4.9 \: {t}^{2} \: \: \: \: - - - (ii)$

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★ On adding equations (i) and (ii), we get

$\sf \: 100 - x + x = 4.9 \: {t}^{2} + 25 \: t - 4.9 \: {t}^{2}$

$\sf \longrightarrow 100 = 25 \: t$

$\sf \longrightarrow t = \cancel\frac{100}{25}$

$\sf \longrightarrow t = 4 \: s$

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Thus, The two Stones will meet after a time of 4 seconds.

☆ Now, From equation (i) we have:

$\sf \: 100 - x = 4.9 \: {t}^{2}$

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Putting t = 4 in this equation, we get:

$\sf \: 100 - x = 4.9 \times {(4)}^{2}$

$\sf \longrightarrow 100 - x = 4.9 \times 16$

$\sf \longrightarrow 100 - x = 78.4$

$\sf \longrightarrow 100 - 78.4 = x$

$\sf \longrightarrow x = 21.6 \: m$

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Thus, the two stones will meet at a height of 21.6 meters from the ground.

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Answer 2

refers in attachment. . . !

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