Physics 1210 – Practice Problems – 2

(Please note that items in bold in the problems below represent vector quantities. The answers are given in italics, within square brackets)

1.) A displacement vector r has a magnitude of r = 175 m and points at an angle of 50 relative to the x-axis. Find the x and y components of the vector.

[134 m; 112 m]

2.) A jogger runs 145 m in a direction 20 east of north and then 105 m in a direction 35 south of east. Determine the magnitude and direction of the resultant vector C for these two displacements.. [+155 m; 29]

3.) Consider two displacement vectors A and B. Vector A points at an angle of 22 above the x axis but has an unknown magnitude. Vector B has an x component of Bx

= 35 m but has an unknown y component By. These two vectors are equal. Find the magnitude of A and the value of By. [37.7 m; 14.1 m]

4.) A small airplane leaves an airport on an overcast day and is later sighted 215 km away, in a direction making an angle of 22 east of north. How far east and north is the airplane from the airport when sighted? [81 km; 199 km]

5.) Consider three vectors:a = 4.2 i 1.5 jb = 1.6 i + 2.9 jc = 3.7 j

The numbers above are in metres. What is the vector sum r of these three vectors? Note that i and j are unit vectors along the x and y directions, respectively.

[2.6 i 2.3 j; 3.5 m at = 319]

6.) What is the angle between the vectors a = 3 i 4 j and b = 2 i + 3 k? Remember that i, j and k are the unit vectors along the x, y and z directions. Use the definition of the dot product to solve this problem. [110]

7.) If a = 3 i – 4 j and b = 2 i + 3 k, what is c = a x b?[c = 12 i 9 j 8 k]