Apologies if this is not a research-specific question, but applied mechanics.
A firefighter has to pass a test in which he is to throw a medicine ball a certain distance. The ball is thrown at a 45 degree angle (Fig. 1) and has to travel a ground distance of 7.5 meters. For the test, a medicine ball is a rough sphere with a mass of 4 kg and ~250 mm in diameter. In preparing for the test, however, the firefighter has only access to a dumbbell, which he does not intend to throw.
Given that a certain force is needed to throw the medicine ball with a preparation phase of 1 m and then released for a 7.5 meter throw, how heavy should the training substitute dumbbell be in order to achieve the equivalent force? Assume that the dumbbell only covers a 1 m distance at 45 degrees and that the firefighter intends to train at a 1 m/s velocity.