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**a person standing on the roof of a 40 m high tower, throws a ball vertically upwards with speed 10m/s. 2 seconds later, he throws another ball again in vertical downward direction(g=10m/s^2) if both hit the ground simultaneously, then choose the correct options.**

a) the first ball hits the ground after 4 seconds.

b) the second ball was projected vertically downwards with speed 5m/s.

c) the distance travelled by the first ball is 10 m greater than the distance travelled by the second ball.

d) both balls hit the ground with same velocities.

$forball2\phantom{\rule{0ex}{0ex}}u,g=10m/{s}^{2},S=40\phantom{\rule{0ex}{0ex}}40=ut+\frac{10*{t}^{2}}{2}\phantom{\rule{0ex}{0ex}}u=10,a=-10m/{s}^{2},S=-40\phantom{\rule{0ex}{0ex}}-40=10\left(t+2\right)-\frac{10*{\left(t+2\right)}^{2}}{2}\phantom{\rule{0ex}{0ex}}t+2=T\phantom{\rule{0ex}{0ex}}-40=10T-\frac{10*{T}^{2}}{2}\phantom{\rule{0ex}{0ex}}{T}^{2}-2T-8=0\phantom{\rule{0ex}{0ex}}{T}^{2}-4T+2T-8=0\phantom{\rule{0ex}{0ex}}T\left(T-4\right)+2\left(T-4\right)=0\phantom{\rule{0ex}{0ex}}T=4sec\phantom{\rule{0ex}{0ex}}optionaiscorrect.\phantom{\rule{0ex}{0ex}}t=4-2=2sec\phantom{\rule{0ex}{0ex}}40=2u+\frac{10*4}{2}\phantom{\rule{0ex}{0ex}}u=10m/s\phantom{\rule{0ex}{0ex}}optionbiswrong\phantom{\rule{0ex}{0ex}}optionCiscorrect.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{sin}cebothhavethesameinitialspeedthevelocitywillbesamewhentheyhit\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}optiondiscorrect.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}regards\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

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