This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Determine the effective acceleration of the ball relative to the lift. The lift is moving down with an acceleration a_lift = 3 m/s^2. The acceleration due to gravity is g = 9.8 m/s^2. Since both the ball (due to gravity) and the lift are accelerating downwards, the acceleration of the ball relative to the lift is the difference between their accelerations. a_relative = g - a_lift a_relative = 9.8 m/s^2 - 3 m/s^2 a_relative = 6.8 m/s^2 Step 2: Identify the initial conditions for the ball's motion relative to the lift. The ball is released, meaning its initial velocity relative to the lift is u = 0 m/s. The distance the ball needs to fall to hit the floor is s = 1.7 m. Step 3: Use a kinematic equation to find the time. We use the equation of motion: s = ut + (1)/(2)a_relativet^2 Since u = 0: s = (1)/(2)a_relativet^2 Rearrange the equation to solve for t: t^2 = (2s)/(a_relative) t = sqrt((2s)/(a_relative)) Step 4: Substitute the values and calculate the time. t = sqrt(2 × 1.7 m)6.8 m/s^2 t = sqrt(3.4 m)6.8 m/s^2 t = sqrt(0.5 s)^2 t ≈ 0.707 s Rounding to two significant figures: t ≈ 0.71 s The ball will take approximately 0.71 s to hit the floor. Last free one today — make it count tomorrow, or type /upgrade for unlimited.