Question

In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the same mass) causes the the pendulum to swing twice as high, 5.2 cm. The second projectile was how many times faster than the first?

Answer 1

The second projectile is
`√(2)` times faster than the first projectile.

Step-by-step explanation:

Mass of first projectile = m

height
`h_(1)` = 2.6 cm

Height
`H_(2)` = 5.2 cm

Let velocity of first projectile = V

Velocity of first projectile = V'

From conservation of momentum principal

m V = (m + m) V'

`V = (m +m)/(m) V'`

V' =
`√(2gH)`

`V = (m +m)/(m) √(2gH)`

Therefore velocity is directly proportional to the height.

`(V_(2) )/(V_(1) ) =\frac{ \sqrt{H_(2) } }\sqrt{H_(1)`

Since
`H_(2) = 2 H_(1)`

`(V_(2) )/(V_(1) ) = √(2)`

Therefore the second projectile is
`√(2)` times faster than the first projectile.