Final answer:
To calculate the horizontal distance (Δx) traveled by the metal sphere, we can use the equations of motion. The correct answer is D. 1.47m.
Step-by-step explanation:
To calculate the horizontal distance (Δx) traveled by the metal sphere, we can use the equations of motion. The horizontal velocity (Vx) of the sphere remains constant throughout its motion.
Using the equation Vx = initial velocity * cos(angle), where the initial velocity is 1.5 m/s and the angle is 20°, we can calculate Vx as Vx = 1.5 m/s * cos(20°).
Next, we use the equation Δx = Vx * t, where t is the time taken to reach the floor. The time can be calculated using the equation h = initial vertical velocity * t + (1/2) * acceleration * t^2, where h is the vertical distance, initial vertical velocity is 1.5 m/s, and the acceleration due to gravity is 9.8 m/s^2. Solving for t gives us t = sqrt(2h/g).
Substituting the given values, we have t = sqrt(2 * 1.2 m / 9.8 m/s^2). Finally, we can substitute the values of Vx and t into the equation for Δx to find the horizontal distance traveled by the metal sphere.
Therefore, the correct answer is D. 1.47m.