SATHEE: Kinematics Question 618

Kinematics Question 618

Question: A body is projected vertically upwards with a velocity u, after time t another body is projected vertically upwards from the same point with a velocity v, where v < u. If they meet as soon as possible, then choose the correct option

Options:

A) $t = \frac{u - v + \sqrt{u^{2} + v^{2}}}{g}$

B) $t = \frac{u - v + \sqrt{u^{2} - v^{2}}}{g}$

C) $t = \frac{u + v + \sqrt{u^{2} - v^{2}}}{g}$

D) $t = \frac{u - v + \sqrt{u^{2} - v^{2}}}{2 g}$

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Answer:

Correct Answer: B

Solution:

[b] Let the two bodies meet each other at a height h after time T of the projection of second body .

Then before meeting, the first body was in motion for time (t + T) whereas the second body was in motion for time T.

The distance moved by the first body in time $(t + T)$

$= u (t + T) - \frac{1}{2} g {(t + T)}^{2}$

And the distance moved by the second body in time $T = v T - \frac{1}{2} g T^{2} = h$ (supposed above) ?(1)

$∴$ The two bodies meet each other.

$∴$ They are equid it’stant from the point of projection.

Hence, $u (t + T) - \frac{1}{2} g {(t + T)}^{2} = v T - \frac{1}{2} g T^{2}$ … (2)

Also from (1) we get, $h = v T - \frac{1}{2} g T^{2}$

$∴ \frac{d h}{d T} = v - g T$

$∴$ h increases as T increases

$∴$ T is minimum when h is minimum i.e., when $\frac{d h}{d t} = 0, i . e ., when v - g T = 0 or T = v / g .$

Substituting this value of T in (2), we get $g t^{2} + 2 t (v - u) + 2 (v - u) (v / g) = 0$

or $t = \frac{2 g (v - u) + \sqrt{4 g^{2} (v - u) + 8 v g^{2} (v - u)}}{2 g^{2}}$

or $t = \frac{u - v + \sqrt{u^{2} - v^{2}}}{g}$

Neglecting the negative sign which gives negative value of t.

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Kinematics Question 618

Question: A body is projected vertically upwards with a velocity u, after time t another body is projected vertically upwards from the same point with a velocity v, where v < u. If they meet as soon as possible, then choose the correct option

Options:

Answer:

Solution:

इंजीनियरिंग की तैयारी

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सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Kinematics Question 618

Question: A body is projected vertically upwards with a velocity u, after time t another body is projected vertically upwards from the same point with a velocity v, where v < u. If they meet as soon as possible, then choose the correct option

Options:

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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