First slide

Projection Under uniform Acceleration

Question

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, travelling with a velocity $ν$ m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity $ν$ of the bullet is

Difficult

A

250 m/s
B

$250 \sqrt{2} m / s$
C

400 m/s
D

500 m/s

Solution

Time taken by the bullet and ball to strike the ground is
$t = \sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 .5}{10}} = 1 s$
Let $ν_{1}$ and $ν_{2}$ be the velocities of ball and bullet after
collision. Then applying,
x = $ν$ t
We have, $20 = v_{1} \cdot 1 or v_{1} = 20 m / s$
$100 = v_{2} . 1 or v_{2} = 100 m / s$
Now, from conservation of linear momentum before and after collision we have,
$0 .01 v = (0 .2.20) + (0 .01.100)$
On solving, we get
v = 500 m / s.

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