Question

Two ball are fired from ground level, a distance d apart. The right one is fired vertically with speed v. At the same time the left ball is fired with speed u and at angle Theta with respect to the ground. What should u and Theta be in order the left ball collides with the right one when the latter reaches its highest point?

Given d, what should v be so that the speed u is minimum?

lu

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Answer #1

Both balls hit each other at maximum height reached and in same time For left ball, In horizontal direction, -ut-at d-u,t In vertical direction, For right ball, Maximum height reached is Time taken to reach maximum height is V- at 0-V-gt

The components of velocities for left ball is d gd it can be seen from above equations involving these variables) Resultant speed is, gd For u to be minimum, differentiate u with respect to Vand equate it to zero (maxima and minima concept)

Direction of firing the projectile should be tan-1 (uy/ux)

Theta = tan-1 (V2/gd)

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