Question

In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.2 cm . A second projectile causes the pendulum to swing twice as high, h2 = 4.4 cm . The second projectile was how many times faster than the first?

Answer 1

here

conservation of energy   p.e = k.e

                                  mgh = 1/2 mv^2 ===> v^2 = 2gh ===> v= sqrt(2gh)

now projectile 1:

                  mgh1 = 1/2 m v1^2

                  mg(2.2) = 1/2 m v1^2 ===> v1 = sqrt(2*g*h1)

         projectile 2:

                   mgh2 = 1/2 mv2^2 ====> v2 = sqrt(2gh2) = sqrt(2g2h1)

               now   v2/v1= sqrt(h2/h1)

                                =sqrt(2h1/h1)

                             v2 = v1*sqrt(2)

            so second projectile is sqrt(2 ) times faster than first projectile