Two spheres A and B, where A has twice the mas of B, are projected at the same horizontal velocity off the edge of two different height shelves. Sphere A leaves from a height of 2.0 m. Sphere B leaves a shelf 1.0 m off the floor. If both spheres leave the edge if the table at the same instant, sphere A will land
A at some point after sphere B
B at the same time as sphere B
C at some time after sphere B
D There is not enough information to decide
Mass has nothing to do with the acceleration due to gravity. tHe lower one hits the Earth first.
D. There is not enough information to decide
In order to determine which sphere will land first, we need to know the horizontal velocity at which both spheres are projected, as well as the impact of air resistance and other factors. Without this additional information, it is not possible to determine which sphere will land first.
To determine which sphere lands first, we need to analyze the motion of each sphere and consider the effect of their different masses and heights.
The time it takes for an object to fall from a certain height can be calculated using the equation:
t = sqrt(2 * h / g)
where t is the time, h is the height, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Let's calculate the time it takes for sphere A to fall from a height of 2.0 m:
tA = sqrt(2 * 2.0 / 9.8) = sqrt(0.408163265) ≈ 0.639 seconds
Now, let's calculate the time it takes for sphere B to fall from a height of 1.0 m:
tB = sqrt(2 * 1.0 / 9.8) = sqrt(0.204081633) ≈ 0.452 seconds
Since sphere B takes less time to fall, it will hit the ground before sphere A.
Therefore, the correct answer is:
C. Sphere A will land at some time after sphere B.