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 laws of motion and the principles of free fall.
First, let's consider the initial velocity (u) of the mass, which is 10 m/s, and the acceleration due to gravity (g), which is approximately 9.8 m/s².
When the mass is projected vertically upwards, it experiences a deceleration due to gravity until it reaches its maximum height. At this point, its velocity becomes zero. The time it takes to reach the maximum height can be calculated using the equation:
t = u / g
Substituting the values, we get:
t = 10 m/s / 9.8 m/s² ≈ 1.02 seconds
Since the time to reach the maximum height is the same as the time to descend from the maximum height to the ground, the total time in the air is approximately 2.04 seconds.
To find the velocity at which the mass hits the ground, we can use the equation for final velocity (v) in free fall:
v = u + gt
Substituting the values, we get:
v = 10 m/s + (9.8 m/s²)(2.04 s) ≈ 10 m/s + 19.992 m/s ≈ 29.99 m/s
Therefore, the mass will take approximately 2.04 seconds to return to the ground, and it will hit the ground with a velocity of approximately 29.99 m/s.