Question

Problem 1 Consider the vectors A, B, aod C drawn below B-10m) (A) Draw a fourth vector D such that the sum of all the components of all the vectors adds t0 zero (A + B + C + D-0). (B) What is the magnitude and direction of the vector? Problem 2 Alice and Bob are studying in Thompson Library, when they realize that they are late for class in Derby Hall. Both students dash out of the front door of the library and head to class across the Oval. Bob jogs at 2.2 m/s straight down the central path for 147 m and then turns 54° to the left in the direction he was heading and jogs straight for an additional 221 m (still at 2.2 m/s) to get to the front door of Derby Hall. Alice cuts across the Oval, walking quite briskly at 1.8 m/s, and takes the direct path to Derby Hall. (See Figure 1 on the next page) (A) How long is Alice's path? NAME

Answer 1

A = 5 cos(90 degree- 20 degree)i^+ 5 sin(90 degree- 20 degree)j^= 5 cos 70i^+ 5 sin 70j^= 1.71i^+ 4.698j^B^rightarrow = 10 Cos 30 degree(- i^) + 10 sin 30 degree(j^) = -8.66 i^+ 5j^c^rightarrow = 4 cos 40 degree i^+ 4 sin 40 degree (- j^) = 3.064i^- 2.571j^d = ? A^rightarrow + B^rightarrow + C^rightarrow + D^rightarrow = 0 D^rightarrow = -A^rightarrow- B^rightarrow- C^rightarrow = -1.71i^+ 4.698j^+ 8.66i^- 5j^- 3.064i^+ 2.541j^= 3.886i^+ 2.269j^magnitude of D^rightarrow = squareroot 3.886^2 + 2.269^2 = 4.5m Let D^rightarrow makes an angle Q with Positive x axis then tan thita = 2.269/3.886 = 0.5838 thita = 30.3 degree