# P2Week5 - P2 Week 5 Solving two equations simultaneously...

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1 P2 Week 5 Solving two equations simultaneously Introduction to Vectors Addition and subtraction of Vectors Two equations for two unknowns If you have N unknowns, in general you at least need N equations to solve them. Example: consider two independent variables x and y. You are given 2=x–y 4=x+y Solution for x is A: 1 B: 2 C: 3 D: 4 E: None of the above

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2 Two equations for two unknowns Example: consider two independent variables x and y. You are given 2=x–y 8=x 2 –y 2 Solution for x is A: 1 B: 2 C: 3 D: 4 E: None of the above Two equations for two unknowns Solving 1D and 2D equations of motion requires solving systems of equations with unknowns occurring as linear or quadratic terms. When you have only two equations, the method of solving this set of equations is simple and requires substituting the relation between the two observables from one equation into the other.
3 1D equation of motion Displacement d = 10 m Acceleration a = –1 m/s 2 Find the initial and final velocities. Do you have enough information to solve this problem? A: Yes B: No Maserati clicker problem Manoj is driving a Maserati and he accelerates uniformly from rest for 1s in first gear. He shifts from first to second gear in 0.5s. Assume that during the shift from 1 st to 2 nd gear, the acceleration is zero. In the second gear he accelerates uniformly with a rate that is 2/3 rd of the rate in the first gear for 3s to reach a speed of 30 m/s. Find the average speed for this 0 to 30m/s (about 68 mph) ride to 2 sig figs. A: 14 m/s B: 16 m/s C: 18 m/s D: 20 m/s E: none of the above

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4 Moejoe Clicker problem Moe needs an orange and an apple to make fruit punch. Joe two floors above throws an apple down from his window with some speed. At the same time Joey one floor below her throws up an orange with the same speed. Moe catches a fruit in each of her outstretched hands (palms up) at the same time. Assume displacement of apple = –2 × displacement of orange and that the apple travels 4m between Joe’s and Moe’s hands. What is the total distance traveled by the orange between hands? g=10m/s 2 . A: 2m B: 2.25m C: 2.5m D: 4.25m E: none of the above Distressed Clicker problem Lady D’Stress sees Batman on the roof of a building and gets to that roof pronto. She then falls from the roof of the building (again). Batman is sick of this behavior and decides to let her fall. However, he comes to his senses in 0.5 sec and dives with an initial speed of 6 m/s. If the distance from roof to ground is 16 m, how far above the ground does Batman catch the Lady? g=10m/s 2 . A: 0.1m B: 0.3m C: 0.5m D: 0.7m E: none of the above
5 Vectors and Scalars A scalar quantity is completely specified by a single value with an appropriate unit and has no direction. A

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P2Week5 - P2 Week 5 Solving two equations simultaneously...

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