1. The pilot of an aircraft flies due north relative to the ground in a wind blowing 50 km/h toward the east. If his speed relative to the ground is 120 km/h, what is the speed of his airplane relative to the air? 2. While her kid brother is on a wooden horse at the edge of a merry-go-round, Sheila rides her bicycle parallel to its edge. The wooden horses have a tangential speed of 6 m/s. Sheila rides at 4 m/s. The radius of the merry-go-round is 8 m. At what time intervals does Sheila encounter her brother, if she rides opposite to the direction of rotation of the merry-go-round? 3. A car is moving at a constant speed of 4 m/s in a circular track of diameter 6 m. (i) calculate the magnitude of the centripetal acceleration, and (ii) if its speed is also increasing at the rate of 5 meters per second per second, what is the tangential acceleration. 4. A race car moving with a constant speed of 50 m/s completes one lap around a circular track in 50 s. What is the magnitude of the radial acceleration of the race car? When the car is directly pointing due North, the brakes are applied, and the speed starts to decrease at the rate of 5 m/s2. What is the tangential acceleration, and the resultant acceleration at this point (give answer in vector notation).