To solve this problem, we can use the equations of motion under constant acceleration. In this case, the motion of the marble can be treated as a projectile motion with constant horizontal velocity and vertical acceleration due to gravity.
Let's calculate the answers to your questions:
A) Time taken to reach the floor: We can use the equation for vertical displacement during free fall:
h = ut + (1/2)gt^2
where: h = vertical displacement (1.50 m) u = initial vertical velocity (0 m/s, as the marble starts from rest) g = acceleration due to gravity (-9.8 m/s^2, assuming downward direction) t = time taken
Rearranging the equation and solving for t, we get:
1.50 = (1/2)(-9.8)t^2
Multiplying both sides by 2/-9.8:
t^2 = (-3.06) t = √3.06 ≈ 1.75 s
Therefore, it takes approximately 1.75 seconds for the marble to reach the floor.
B) Initial speed: To find the initial speed of the marble, we can use the equation for horizontal displacement:
d = vt
where: d = horizontal displacement (2.0 m) v = initial horizontal velocity (the same value throughout the motion) t = time taken (1.75 s)
Rearranging the equation and solving for v, we get:
v = d / t v = 2.0 m / 1.75 s v ≈ 1.14 m/s
Therefore, the initial speed of the marble is approximately 1.14 m/s.