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: Define free fall (3.1). Free fall is the motion of an object solely under the influence of gravity, neglecting any other forces such as air resistance. Step 2: Determine the time the ball is in contact with the floor before the first bounce (3.2.1). From the graph, the ball first hits the floor (position = 0 m) at approximately t_1 = 0.60 s. The ball leaves the floor after the first bounce (position starts increasing from 0 m) at approximately t_2 = 0.64 s. The time in contact with the floor is the difference between these two times. t_contact = t_2 - t_1 = 0.64 s - 0.60 s = 0.04 s Step 3: Determine the time it takes the ball to reach its maximum height after the first bounce (3.2.2). The ball leaves the floor after the first bounce at t_leave = 0.64 s. The maximum height after the first bounce occurs at the peak of the first arc, which is at t_peak = 1.00 s. The time taken to reach maximum height is the difference between these two times. t_max\_height = t_peak - t_leave = 1.00 s - 0.64 s = 0.36 s Step 4: Determine the speed at which the ball leaves the floor at the first bounce (3.2.3). We use the kinematic equation v_f = v_i + a t. At the maximum height, the final velocity v_f = 0 m/s. The acceleration due to gravity a = -9.8 m/s^2 (taking upwards as positive). The time taken to reach maximum height t = 0.36 s (from Step 3). 0 = v_i + (-9.8 m/s^2)(0.36 s) v_i = 9.8 m/s^2 × 0.36 s v_i = 3.528 m/s Rounding to two decimal places, the speed is 3.53 m/s. Step 5: Determine the time t indicated on the graph (3.2.4). The time 't' indicated on the graph corresponds to the moment the ball hits the floor for the second time (where its position is 0 m after the first bounce). From the graph, this occurs at t = 1.60 s. 3.1: Free fall is the motion of an object solely under the influence of gravity, neglecting air resistance. 3.2.1: The time that the ball is in contact with the floor before the first bounce is 0.04 s. 3.2.2: The time it takes the ball to reach its maximum height after the first bounce is 0.36 s. 3.2.3: The speed at which the ball leaves the floor at the first bounce is 3.53 m/s. 3.2.4: Time t indicated on the graph is 1.60 s. 3 done, 2 left today. You're making progress.