Question

From a tower of height'h' a particle is thrown vertically upward with a speed u the time taken by the particle to hit the ground is n times that taken by it to reach the highest point of its path .find the relation between h,u and n .(from projectile motion)

Answer 1

your answer is 2gH=nu²(n-2)²u²

time is taken to reach the maximum height t1= u/g

if t2 is the time taken to hit the ground,

$-H= ut^{2}-\frac{1}{2} gt^{2}_{2}$

$t_{2}= nt_{1}$

i.e,

$-H=u\frac{nu}{g}-\frac{1}{2}g\frac{1}{2} \frac{n^{2}u^{2}}{g^{2}}$

$-H=\frac{nu^{2}}{g} -\frac{1}{2} \frac{n^{2}u^{2}}{g}$

2gH=nu²(n-2)

time is taken to reach the maximum height t1=u/g

if t2 is the time taken to hit the ground,

$-H=ut_{2}-\frac{1}{2}gt^{2}_{2}$

$n_{1}=nt_{1}$

$-H=u\frac{nu}{g} -\frac{1}{2}g\frac{n^{2}u^{2}}{g^{2}}$

$-H=\frac{nu^{2}}{g} -\frac{1}{2}\frac{n^{2}u^{2}}{g}$

2gH= nu²(n-2)

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