Physics, asked by divit26, 9 months ago

There are two values of time for which a projectile is at the same height. The sum of these two times is equal to (T= time of flight of the projectile)

Answers

Answered by nirman95
19

Given:

There are two values of time for which a projectile is at the same height.

To find:

Sum of the two times.

Calculation:

Let that specified height be h ;

h = u_{y}t -  \dfrac{1}{2} g {t}^{2}

 =  > h =  \{u \sin( \theta) \} t -  \dfrac{1}{2} g {t}^{2}

 =  > 2h =  2\{u \sin( \theta) \} t -  g {t}^{2}

 =  > g {t}^{2} -  2u \sin( \theta) t  + 2h = 0

Let the two roots be t1 and T2 when this height h is obtained ; Therefore sum of roots will be :

 \therefore \: t1 + t2 =  -   \dfrac{b}{a}

 =  >  \: t1 + t2 =  -  \bigg(  \dfrac{ - 2u \sin( \theta) }{g}  \bigg)

 =  >  \: t1 + t2 =    \dfrac{ 2u \sin( \theta) }{g}

 \boxed{ \sf{ =  >  \: t1 + t2 =    \dfrac{ 2u \sin( \theta) }{g}   = T}}

Hope It Helps.

Answered by atharvanihul123
3

Answer: T

Explanation:

Time taken to go from O to A = t1

Time taken to go from O to B = t2

Also ,

Time taken to go from O to A = time taken to go from B to D

Therefore, t1 +t2 = t2 + time taken to go from B to D

= T

Thank you

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