A railroad flatcar is traveling to the right at a speed of 13.0 m/s relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (?Fig. E3.30?). What is the velocity (magnitude and direction) of the scooter relative to the flat-car if the scooter’s velocity relative to the observer on the ground is (a) 18.0 m/s to the right? (b) 3.0 m/s to the left? (c) zero?

Solution 32E Step 1 of 3: What is the velocity (magnitude and direction) of the scooter relative to the flat-car if the scooter’s velocity relative to the observer on the ground is (a) 18.0 m/s to the right Here since the speeds are very less compared to speed of light, we can use normal velocity vector addition; The speed of the scooter relative to flat-car(moving) v scooterflatcar scooterground vflatcarground Where v scooterflatcar the speed of the scooter relative to flat-car(moving) v is the speed of scooter relative to ground. scooterground v is the speed of flatcar relative to ground. flatcarground Using v scooterground8 m/s and v flatcarground13 m/s in above equation, v scooterflatcar3 m/s 13 m/s v scooterflatcar m/s Since to the right is taken as positive.As the velocity of scooter relative to flatcar is also positive, which means it is 5 m/s towards right. Step 2 of 3: (b) 3.0 m/s to the left The speed of the scooter relative to flat-car(moving) vscooterflatcarv scooterground vflatcarground Where vscooterflatcar the speed of the scooter relative to flat-car(moving) v is the speed of scooter relative to ground. scooterground vflatcargrounds the speed of flatcar relative to ground. Using v scooterground - 3 m/s and v flatcarground13 m/s in above equation, vscooterflatcar 3 m/s 13 m/s v = 16 m/s scooterflatcar Since to the right is taken as positive.As the velocity of scooter relative to flatcar is negative, which means relative velocity of scooter relative to flat car is 16 m/s towards left.