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 the pendulum to swing higher, to h2 = 5.4 cm. the second projectile was how many times faster than the first?

Answer 1

The height is proportional to the kinetic energy of the projectile. So the ratio of the two KEs is 5.4/2.2 = 2.45.

KE is proportional to velocity squared, so velocity is proportional to the square root of the KE, which is √2.45 = 1.57, which is the answer.


To explain it more in detailed:

KE = PE = mgh, which displays you the KE and height proportionality.

KE = ½mV² or

V = √(2KE/m) which shows you the other proportionality

combining

V = √(2mgh/m) = √(2gh)

V₁/V₂ = √(2gh₁) / √(2gh₂) = √(h₁/h₂) = √(5.4/2.2) = 1.57