Let Shot that shot

Classical Mechanics Level 3

A Balls projected from the of a building with speed u at an angle x from horizontal (see figure). A bullet is fired horizontally from a point A, when the ball is in the horizontal level of the point A. If the bullet hits the ball in air, the time interval between the projection of the ball and the firing of bullet is: (g-- acceleration due to gravity) Assume no other forces.

data insufficient 2u sin(x)/3g u sin(x)/2g u sin(x)/g

2 solutions

Ujjwal Rane
Oct 19, 2014

Consider just the vertical motion:

When the bullet is fired, the ball could be:

moving up or down or
momentarily at rest

Consider the two objects as dropped simultaneously from elevation of point A. Both will be equally affected by gravitational acceleration (g).

But in case 1 the ball is dropped with some initial velocity (upward or downward) so the bullet can never catch up with it in the vertical direction!

So for the hit, only possibility 2 would work, making elevation of A as the max height attained by the ball

Substitute:

v = 0 at the highest point; u = u sin(x) and a = -g

in equation: v = u + at

to get t = time to reach the max height $=u sin(x)/g$

Akash Pachauri
May 6, 2014

as, accn. of projectile w.r.t. bullet after firing the bullet will be zero. so, for collision, velocity of bullet w.r.t. projectile must be along the line joining them. this is only possible when height of A is equal to the maximum height of projectile where both bullet and projectile have velocity along horizontal. means bullet must be fired at the instant when projectile reached at its highest point. So, time lag= u sin(x)/g

Let Shot that shot

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