Taking X -axis along horizontal and Y -axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point ( 30m, 40m ) ? Take g = 10ms^ - 2

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Quantrex Academy · Accepted Answer

Correct answer: B. 30ms^ - 1

Using equation of trajectory for a projectile motion :

y = xtan \theta - \dfrac{gx^{2}}{2u^{2}} \left(1 + \tan^{2} \theta\right)<br /><br />For the projectile to pass through (30 m, 40 m) :<br /><br />\text{40} = \text{30 tan} \text{\alpha} - \dfrac{{g (30)}^{2}}{{2u}^{2}} \left(1 + \tan^{2} \text{\alpha}\right)<br /><br />or \text{ and } \text{ and } 900\tan^{2}\alpha - (6u^{2}tan\alpha ) + (900 + 8u^{2} ) = 0

For real value of \alpha. The discriminant of a quadratic equation

b^{2} - 4ac ≥ 0

& & & & & & & &

( 6u^{2}{)}^{2} ≥ 3600 ( 900 + 8u^{2} )

or &

( u^{4} - 800u^{2} ) ≥ 9, 00, 00

or & &

( u^{2} - 400{)}^{2} \ge (2, 50, 000 )

or & & &

u^{2} - 400 ≥ 500

or & &

u^{2} ≥ 900

or

u ≥ 30ms^{- 1}

Taking X -axis along horizontal and Y -axis along vertical, with...

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