Energy convertion and Galelios law

hi can you help me with this questions. i was quite confused as i confused this question with Galelios law that object with different mass falls at a same rate. but seems like its not.

Q) much to Altheas dismay, pearl and Isla decide to use a ball machine to shoot water filled tennis balls over the house, at the same speed and the same angle and same height. the conditions are identical excpet that the ball now has mass of 0.200kg. discuss how the increased mass will affect the energy and the flight path of the ball.

Hi @Anne,

For any explain or discuss questions, it can be really useful to use one or more equations to support your answer. I assume that the question is asking us to compare water filled vs empty tennis balls.

In this case you’ll notice that no kinematic equations (the ones describing projectile motion eg. vf=vi+at) refer to mass. As the question tells us that the only variable to be changed is mass, the launch velocity, launch angle, and launch height must all remain constant. As such, the flight path will not be affected (both accelerate at -9.8ms^-2, and maintain the same horizontal velocity throughout their flight - ignoring air resistance).

However kinetic energy is given by Ek=1/2mv^2
This equation does include mass. We can see that inreasing the mass would also increase the kinetic energy. The larger mass would also mean that the projetile would have more gravitational potential energy when at the same height as the lower mass object (Ep=mgh).

In summary, the flight path would be exactly the same for both objects, but the kinetic energy would be higher for the projetile with more mass.