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Question

A body is projected vertically up with velocity u. Its velocity at half its maximum height is?


A

2u

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B

u2

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C

u2d

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D

u22

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Solution

The correct option is B

u2


Step 1: Given data

A body is projected vertically up with velocity u

Step 2: Formula used

Hmax=u22g[whereHmax=maximumheightattainedbytheprojectile,u=initialvelocity,g=accelerationduetogravity]

Step 3: Calculating velocity at half its maximum height

Use the third kinematical equation to determine the velocity of the body at half of its maximum height as follows,

v2=u2+2aswherev=finalvelocityatitshighestpoint,u=initialvelocity,a=acceleration,s=totalupwarddistance]

The acceleration produced in a body propelled upward is called acceleration owing to gravity. Assuming that the upward direction is positive, the acceleration owing to gravity has a negative sign because it acts in the downward direction.

Therefore, the above equation becomes v2=u2-2gh[h=maximumheightattained]............(i)

As we need to determine the velocity at half of the maximum height, substitute h=Hmax2

Hmax=u22gh=u24g

Substituting the value of h=u24g in equation (i)

v2=u2-2gu24gv2=u2-u22v2=u22v=u2

Hence, option B is the correct answer.


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