Sphere A is projected off the edge of a 2 m bench with a horizontal velocity of 10 m/s. Sphere B is dropped from the same height as Sphere A. Both spheres have the same size and mass. At the instant before it hits the floor, will the velocity of Sphere A be less than, greater to or the same as the velocity of Sphere B. Explain why.
The velocity of Sphere A will be the same as the velocity of Sphere B at the instant before they hit the floor.
This can be explained by considering the factors that affect the motion of each sphere. Sphere A is projected off the edge of the bench with a horizontal velocity of 10 m/s. However, this horizontal velocity does not affect the vertical motion of the spheres. Both spheres will experience the same acceleration due to gravity as they fall from the same height.
When an object is dropped from a height, its initial vertical velocity is always zero. Therefore, Sphere A and Sphere B have the same initial vertical velocity. As they fall, both spheres will accelerate downwards due to gravity. Since both spheres have the same mass, they will experience the same gravitational force and therefore the same acceleration.
Due to this equal acceleration, both spheres will have the same increase in velocity as they fall. As a result, at the instant before they hit the floor, Sphere A and Sphere B will have the same vertical velocity, making their final velocities equal.