Final answer:
To make two objects with different masses reach the target at the same time without the influence of air resistance, they should be launched with the same initial velocity. This is because the acceleration due to gravity is constant and does not depend on the mass of the objects. Exerting the same force to give them equivalent initial velocities fulfills this condition.
Step-by-step explanation:
To ensure that both objects with different masses reach the target at the same time, it is important to understand the concepts of gravity and acceleration. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This implies that, in the absence of air resistance, two objects dropped from the same height will hit the ground at the same time, regardless of their mass, because the acceleration due to gravity is the same for both objects (approximately 9.81 m/s2 on Earth).
Therefore, if the objective is to make sure that both objects reach the target at the same time when thrown horizontally, one does not need to exert different forces on them. Instead, they should be given the same initial velocity in the horizontal direction. In practice, this means simply throwing or launching them with the same speed; the differing masses will not affect the time it takes for them to reach the target. If, however, external forces such as air resistance are significant, then the object with less mass may require guidance to ensure it doesn't slow down more quickly than the more massive object.
In summary, when ignoring air resistance, exert the same force on the two objects to give them the same initial velocity, and they will reach the target simultaneously, irrespective of their mass differences, in accordance with Newton's laws of motion.