One of the Best Veog from 1.6 Estrnales and Order-O·Magnitude Calculations 132-3

Question

One of the Best Veog from 1.6 Estrnales and Order-O·Magnitude Calculations 132-381 A right triangle has a hypotenuse of length 2.30 m, and one of its angles is 40.0°, What are the lengths of the following sides? (a) the side opposite the 40.0° angle (b) the side adjacent to the 40.0° angle 13. Question from 1.7: Coordinate Systems (39-44 Vector A has a magnitude of 27 units and points in the positive y-direction. When vector B is added to A, the resultant vector A + B points in the negative y-direction with a magnitude of 19 units. Find the magnitude and direction of B. magnitude unit(s) 14. Question from 1.7:Coordinate Systems (39-44 A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0° above the horizontal. Next, it travels 135 ft at an angle of 40.0° below the horizontal. Use graphical techniques to find the roller coaster's displacement from its starting point at the end of this movement. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen @ ^..Ga usasts Type here to search

Explanation / Answer

Given

12

right angle triangle of hypotenus length is h = 2.30 m

the angle theta = 40 degrees

we know from Trigonometry in a right angle triangle

sin theta = opposite side / hypotenus

and cos theta = adjacent side / hypotenus

for opposite side

sin theta = opposite side / hypotenus

opposite side = sin theta * hypotenus

oppisite side = sin40*2.3 m = 1.478 m

and the adjacent side is  

cos theta = adjacent side / hypotenus

adjacent side = cos theta*hypotenus

= cos 40*2.3 m = 1.7619 m

13

Vector A has magnitude of 27 units along + y direction

when vector B is added then the resultant vector is 19 units along -ve y direction

that is 27+x = 19 ==> x = 19+27 m = 46 m

so the magnitude of aalong the -y direction is 46 m

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