Question

. A number of bullets are fired horizontally with different velocities from the top of a tower they

reach the ground [ ]

a) at same time with same velocity
b) at different time with different velocities

c) at same time with different velocities
d) at different times with same velocity​

Answer 1

They reach the ground at same time with different velocities. hence correct option is (c).

A number of bullets are fired horizontally with different velocities from the top of a tower, they reach the ground..

1. (a) at the same time with same velocity
2. (b) at different time with different velocities
3. (c) at same time with different velocities
4. (d) at different times with same velocity

Let a bullet is projected horizontally with speed u, it strikes the ground at a distance x after time t from the tower of height h.

Final velocity of the bullet is given by,

$v=u\hat i+(-gt)\hat j$

Here you can observe that the final velocity of a bullet fired horizontally depends upon the initial velocity of the bullet. hence bullets with different velocities will reach the ground with different velocities.

For vertical motion,

$h=\frac{1}{2}gt^2$

Here you see that the time taken by bullet depends on the height of tower. but here, all bullets are fired from the same top of tower. i.e., the height of tower remains constant. so the time remains constant. Hence all the bullets will reach the ground at same time.

Therefore they reach the ground at same time with different velocities.

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