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 the velocities with respect to the ground. Let's consider the direction from the patient towards the dentist as the positive direction. Velocity of the dentist (v_D): The dentist moves towards* the patient. This means the dentist is moving in the negative direction relative to our chosen positive direction. v_D = -0.5 ms^-1 Velocity of the patient (v_P): The patient reclines backwards*. This means the patient is moving away from the dentist, which is also in the negative direction. v_P = -0.2 ms^-1 Step 2: Calculate the velocity of the dentist relative to the patient. The relative velocity of object A with respect to object B is given by v_AB = v_A - v_B. Here, we want the velocity of the dentist relative to the patient (v_DP). v_DP = v_D - v_P Substitute the values: v_DP = (-0.5 ms^-1) - (-0.2 ms^-1) v_DP = -0.5 ms^-1 + 0.2 ms^-1 v_DP = -0.3 ms^-1 Step 3: Determine the speed. Speed is the magnitude of velocity. Speed = |v_DP| = |-0.3 ms^-1| Speed = 0.3 ms^-1 The dentist's speed relative to the patient is 0.3 ms^-1.