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Standard XII

Mathematics

Definite Integral as Limit of Sum

If usinx + vc...

Question

If usinx + vcosx=5 anf ucosx-vsinx=7 then u"v' - u'v" equals (the differential is with respect to x) A) - 74(v')³/u³ B) 74 v (v')²/u³ C) 1 D) 74u (v')²

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A projectile is fired with velocity V making the angle x with the horizontal. what is the change in velocity when it is at the highest point?

At the highest point the velocity of the object will be u cos(x). And intially the velocity will be u. And u = root (u²sin²x+u²cos²x).

Now required ∆u= u cos x - u

Here we cannot say, because the horizontal component of velocity remains constant And only the vertical component of velocity changes, that u sin x vanishes, so ∆u=u sin x. Because u is not equal to u sin x + u cos x, but is equal to the resultant of u sin x and u cos x. But in the test in the projectile chapter my answer tuemed out to be Wrong. Why?

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