A projectile is thrown from a point O on the ground at an angle $$45o$$ from the vertical and with a speed $$52m/s$$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down the ground, $$0.5$$ s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity g $$=10$$ $$m/s2$$.The value of t is $$_______The$$ value of x is $$_______$$

Question

A projectile is thrown from a point O on the ground at an angle $$45o$$ from the vertical and with a speed $$52m/s$$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down the ground, $$0.5$$ s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity g $$=10$$ $$m/s2$$.The value of t is $$_______The$$ value of x is $$_______$$

Infinity Learn · Accepted Answer

→from O to H time of ascent $$=Uyg=510=0.5sec$$→at highest point $$mvx=m2vx1vx1=10$$ $$m/s$$→ one part A of mass $$m/2$$ is falling vertically down in $$0.5$$ $$sec$$⇒ part B is not having vertical component of velocity, it is falling freely in gravity⇒$$t=0.5secOQ=OP+PQ=5$$×$$0.5+10$$×$$0.5=7.5m$$→from O to H time of ascent $$=Uyg=510=0.5sec$$→at highest point $$mvx=m2vx1vx1=10$$ $$m/s$$→ one part A of mass $$m/2$$ is falling vertically down in $$0.5$$ $$sec$$⇒ part B is not having vertical component of velocity, it is falling freely in gravity⇒$$t=0.5secOQ=OP+PQ=5$$×$$0.5+10$$×$$0.5=7.5m$$

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