16. Solve the following triangles using SOHCAHTOA and Pythagoras. Show all work. a. In the figure below, the 4.0 meter ladder makes a 60. degree angle with the ground. y 4.0 m 600 i. How high does the ladder reach? ii. How far is the base of the ladder from the wall? c. Solve for x, y, and A. 8 45 d. Solve for BC and the total height 1.5 meters 24 C 60 meters 18. We can only add and subtract numbers in Physics if they have the same units. For example, I can add 5.0 m to 12 m to get 17 m, but I cannot add 5.0 m to 10 m/s. You cannot add a velocity (10 m/s) to a distance (5 m) and get anything meaningful. Use dimensional analysis (see the video in lessons) to ensure that the kinematic equations shown below adhere to this rule. (Note: it does not matter at this stage if you understand the physics behind the equations). The units for each variable are given. The first one is done for a. V = v + at Answer: Variable Units d m Vi m/s Vf m/s a m/s t S V = V + at Step 1: replace each variable with units only [m/s] = [m/s] + [m/s][s] Step 2: cancel and simplify where possible [m/s] = [m/s] + [m/s][s] Step 3: compare resulting terms (same?) |[m/s] = [m/s] + [m/s] Conclusion: since each term has the units of m/s, the equation is likely valid b. v = dt c. d = vit+at (the does not have a unit so is not considered) 19. Describe how you can recognize a positive vs. a negative vs a zero slope on a graph. Sketch and explain. 12. Evaluate the following and use the correct number of significant figures in your answer (Show all work) a. 2.35 cm x 4.6 cm b. 4/3 (3.14159)(4.7 in) C. d. (-1.25 m) (3.2 m) 3.4 m 33560000000 x .00000012 km 24.5 hr e. 2301 cm + 834.12 cm + 9.0 cm (Answer: 3144 cm, the max precision is the one's place of 2301 cm) 13. Summarize the difference between the rules for significant figures when adding/subtracting and multiplying/dividing. 14. Solve for x in the following equations (show all work): a. 2 = 5 + x b. 192x+7 c. 3-5x=14 d. 5 = x 2 15. Rearrange the equation, solving for the variable shown (clearly show all steps). a. Solve for Q where F 1 = 2 r 2 b. Solve for t where d = at' v + v c. Solve for V. where Vo d = t d. Solve for a where 2 v = v + 2ad d-d e. Solve for d, where f i = t - t f. Solve for m where E = mgh Ep g. Solve for m where EK = 1/2mv h. Solve for t; where i. j. Solve for vo where Solve for v; where Vi k. Solve for V, where I. Solve for v where == d - d. t-t i i d = vot + at v, 2 = v, + 2ad d = v + v 0 2 EK = 12mv t