Please provide complete solutions to the following problems. Your solutions must include communication as to your steps and diagrams where appropriate. Express your final answers with the correct number of significant digits, units, and vector direction as appropriate.
1. A worker drops his hammer while working on your building. You observe as the falling hammer takes 0.20 s to fall past your window. The window is 1.6 m tall. From what height above the top of the window was the hammer dropped by the worker?
2. A rock is dropped from rest into a deep well. A splash is heard 3.1 s later. If the speed of sound is 345 m/s, what is the displacement of the rock?
3. You are driving. As you turn onto Greenbank Road from a side street with a stop sign, an OC Transpo bus going 50 km/h passes you in the adjacent lane. You want to get ahead of the bus before the next traffic light, which is two blocks away. Each block is 70m long and the side streets are 10 m wide. If you can increase your speed at a rate of 7 km/h each second, can you get ahead of the bus? Use a diagram in your answer and state all of your assumptions.
4. A truck travelling south on Highway 416 changes their velocity from 9.6 m/s [S] to 9.6 m/s [S 35° W] in 10.0 s. Determine the acceleration of the truck.
5. A navigator directs a ship from an initial position 25 km [32° E of N] of a lighthouse to a position 18 km [10° S of W] of the lighthouse. If the journey takes 1.4 h, determine the velocity of the ship.
6. A ball is thrown at a speed of 30 m/s at an angle of 50° up from the horizontal. 3.0 s later, its speed is 20.3 m/s at an angle of 18.4° below the horizontal. Show that its acceleration (magnitude and direction) is that due to gravity (i.e. 9.8 m/s² [down]).
7. A golf ball is launched from the roof of a school with a velocity of 20 m/s at an angle of 30° above the horizontal. If the roof is 40 m above the ground, calculate the ball's time of flight and its horizontal displacement when it lands.
8. A fighter jet going at 350 km/h dives at an angle of 25° from the vertical. If it drops a bomb from a height of 200 m, how far will the bomb travel horizontally, and what will be its velocity just before it hits the ground?
9. A Rotating Space Station (RSS) has long been an idea to simulate gravity in Earth's orbit. The RSS would serve a purpose to provide space travellers with gravitational acceleration that would equal that of the gravity on Earth (1 g), on Mars (.37 g), and Earth's Moon (.17 g). Suggest a possible design which might accommodate all 3 needs. Determine the period and frequency of the rotation of your RSS design.
10. Determine the acceleration of planet Jupiter around the sun. Perform appropriate research to find the data you require to accomplish this calculation.