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, the velocity of sphere A will be greater than that of Sphere B. Explain why
The velocity of an object can be broken down into two components: horizontal and vertical. In this case, Sphere A is projected off the edge of the bench with a horizontal velocity of 10 m/s and will also have a vertical velocity due to the force of gravity.
Sphere B, on the other hand, is only dropped vertically from the same height. Therefore, it will only have a vertical velocity component due to gravity.
Since Sphere A has a horizontal velocity component in addition to the vertical component, it will have a greater velocity overall compared to Sphere B just before it hits the floor.
This can be understood by considering that the horizontal velocity of Sphere A adds to its overall speed, while Sphere B only falls vertically and is not affected by the horizontal component of velocity. However, it is important to note that both spheres will have the same vertical velocity due to gravity alone.