When a body is projected vertically upward then its velocity is?

In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.

Answer

Verified

Hint: Use the formula for the maximum height attained by the projectile. Then use the kinematic equation relating final velocity, initial velocity, acceleration and displacement to substitute half of the maximum height for the displacement in the kinematic equation.

Formula used:

\[{H_{\max }} = \dfrac{{{u^2}}}{{2g}}\]Here, u is the initial velocity of the projectile and g is the acceleration due to gravity.

Complete step by step answer:

We know that the maximum height attained by the projectile projected vertically upward is,\[{H_{\max }} = \dfrac{{{u^2}}}{{2g}}\] …… (1)Here, u is the initial velocity of the projectile and g is the acceleration due to gravity.Use the third kinematical equation to determine the velocity of the body at half of its maximum height as follows,\[{v^2} = {u^2} + 2as\]Here, v is the final velocity of the body at its highest point, a is the acceleration of the body and s is the total upward distance covered by the body.For a body projected in the upward direction, the acceleration produced in the body is acceleration due to gravity. Let upward direction be the positive direction, therefore, the acceleration due to gravity has the negative sign as it is acted in the downward direction. Therefore, the above equation becomes,\[{v^2} = {u^2} - 2gh\] …… (2)Here, h is the maximum height attained by the body.As we need to determine the velocity at half of the maximum height, substitute \[h = \dfrac{{{H_{\max }}}}{2}\] in equation (1).\[h = \dfrac{{{u^2}}}{{4g}}\]Substitute \[h = \dfrac{{{u^2}}}{{4g}}\] in equation (2).\[{v^2} = {u^2} - 2g\dfrac{{{u^2}}}{{4g}}\]\[ \Rightarrow {v^2} = {u^2} - \dfrac{{{u^2}}}{2}\]\[ \Rightarrow {v^2} = \dfrac{{{u^2}}}{2}\] \[\therefore v = \dfrac{u}{{\sqrt 2 }}\]

So, the correct option is (D).

Note: In vertical projectile motion, the velocity of the body at its maximum height becomes zero. In this case, we are calculating the velocity of the body at half of the maximum height. Do not substitute 0 for v in the final equation.

Q&A When

When a body is projected vertically upward then its velocity is?

zusammenhängende Posts

Werbung

NEUESTEN NACHRICHTEN

Toplisten

Werbung

Populer

Token Data

Werbung

Um

Legal

Hilfe

Sozial