SATHEE: Kinematics 2 Question 4

Kinematics 2 Question 4

6. From a tower of height $H$ , a particle is thrown vertically upwards 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. The relation between $H, u$ and $n$ is

(a) $2 g H = n^{2} u^{2}$

(b) $g H = (n - 2)^{2} u^{2}$

(d) $g H = (n - 2)^{2} u^{2}$

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Answer:

Correct Answer: 6. (c)

Solution:

Time taken to reach the maximum height, $t_{1} = \frac{u}{g}$

If $t_{2}$ is the time taken to hit the ground, then

$\begin{aligned} i.e. & - H & = u t_{2} - \frac{1}{2} g t_{2}^{2} \\ But & t_{2} = n u_{1} \\ So, & - H & = u \frac{n u}{g} - \frac{1}{2} g \frac{n^{2} u^{2}}{g^{2}} \\ - H & = \frac{n u^{2}}{g} - \frac{1}{2} \frac{n^{2} u^{2}}{g} \\ \Rightarrow & 2 g H & = n u^{2} (n - 2) \end{aligned}$

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Kinematics 2 Question 4

6. From a tower of height H, a particle is thrown vertically upwards 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. The relation between H,u and n is

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6. From a tower of height $H$ , a particle is thrown vertically upwards 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. The relation between $H, u$ and $n$ is