Kinematics Question 171

Question: A projectile is fired vertically upwards with an initial velocity $ u $ . After an interval of T seconds, a second projectile is fired vertically upwards, also with initial velocity $ u $ .

Options:

A) They meet at time $ t=\frac{u}{g} $ and at a height $ \frac{u^{2}}{2g}+\frac{gT^{2}}{8} $

B) They meet at time $ t=\frac{u}{g}+\frac{T}{2} $ and at a height $ \frac{u^{2}}{2g}+\frac{gT^{2}}{8} $

C) They meet at time $ t=\frac{u}{g}+\frac{T}{2} $ and at a height $ \frac{u^{2}}{2g}-\frac{gT^{2}}{8} $

D) They never meet

Show Answer

Answer:

Correct Answer: C

Solution:

[c] For first projectile, $ h _{1}=ut-\frac{1}{2}gt^{2} $ For second projectile,

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

When both meet i.e. $ h _{1} $ = $ h _{2} $ : $ ut-\frac{1}{2}gt^{2}=u(t-T)-\frac{1}{2}g{{(t-T)}^{2}} $
$ \Rightarrow uT+\frac{1}{2}gT^{2}=gtT\Rightarrow t=\frac{u}{g}+\frac{T}{2} $

And $ h _{1}=u( \frac{u}{g}+\frac{T}{2} )-\frac{1}{2}g{{( \frac{u}{2}+\frac{T}{2} )}^{2}}=\frac{u^{2}}{2g}-\frac{gT^{2}}{8} $



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