1. A student drives south at 80m/s for four minutes, then turns west and drives at 100m/s for five minutes, and finally travels northwest at 120m/s for three minute. For this twelve minutes trip, find (a)the total vector displacement, (b) the average speed, and (c) the average velocity.

To solve this problem, we need to break down the trip into its components and calculate each part separately.### (a) Total Vector Displacement1. **Southward Displacement:** - Speed = 80 m/s - Time = 4 minutes = 240 seconds - Displacement = Speed × Time = south2. **Westward Displacement:** - Speed = 100 m/s - Time = 5 minutes = 300 seconds - Displacement = Speed × Time = west3. **Northwestward Displacement:** - Speed = 120 m/s - Time = 3 minutes = 180 seconds - Displacement = Speed × Time = northwest Since northwest is at a 45-degree angle, we can split this into north and west components: - North component = \(21600 \, \text{m} \times \cos(45^\circ) = 15273.6 \, \text{m}\) - West component = \(21600 \, \text{m} \times \sin(45^\circ) = 15273.6 \, \text{m}\)**Total Displacement Components:**- South-North Component: - West Component: **Resultant Displacement:**Using Pythagorean theorem: The direction can be found using: ### (b) Average SpeedAverage speed is the total distance traveled divided by the total time.- Total distance = - Total time = 12 minutes = 720 seconds ### (c) Average VelocityAverage velocity is the total displacement divided by the total time. The direction is the same as the total vector displacement, approximately south of west.