To determine the time it takes for the mass to return to the ground and the velocity at which it hits the ground, we can use the equations of motion.
When the mass is projected vertically upwards, the initial velocity (u) is 10 m/s, and the final velocity (v) when it reaches the ground is 0 m/s (since it comes to a stop). The acceleration (a) acting on the mass is the acceleration due to gravity, which is approximately -9.8 m/sĀ² (negative because it acts in the opposite direction to the motion).
We can use the following equation to find the time (t) it takes for the mass to return to the ground:
v = u + at
0 = 10 - 9.8t
Solving this equation for t:
9.8t = 10
t = 10 / 9.8
t ā 1.02 seconds
So, it takes approximately 1.02 seconds for the mass to return to the ground.
To find the velocity at which it hits the ground, we can use the equation:
v = u + at
v = 10 - 9.8 * 1.02
v ā 10 - 9.996
v ā 0.004 m/s
Therefore, the velocity at which the mass hits the ground is approximately 0.004 m/s.