Final answer:
To find the range of the stone thrown upwards from the lift floor, calculate the time it takes to reach the highest point, and then use the horizontal component of the initial velocity to find the range.
Step-by-step explanation:
To find the range of the stone thrown upwards from the lift floor, we first need to calculate the time it takes for the stone to reach its highest point. We can use the vertical component of the stone's initial velocity and the acceleration due to gravity to find this time. The initial vertical velocity of the stone is given by v_y = 4 m/s * sin(15°) and the acceleration due to gravity is -9.8 m/s². Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for t:
v = u + at
-v_y = 0 + (-9.8) * t
t = v_y / 9.8
Substituting the values, t = (4 m/s * sin(15°)) / 9.8 m/s² = 0.0278 s.
Now we can calculate the range of the stone. The horizontal component of the stone's initial velocity is given by v_x = 4 m/s * cos(15°). The acceleration of the lift does not affect the horizontal motion of the stone. Therefore, the range can be calculated using the equation d = v_x * t, where d is the range, v_x is the horizontal component of the velocity, and t is the time it takes to reach the highest point:
d = (4 m/s * cos(15°)) * 0.0278 s = 0.106 m.
So, the range of the stone is approximately 0.106 meters, which is closest to option a) 3m.