finding displacement, speed and velocity

[Clifford]

A runner runes in a straight line of 850 m [25 degrees N of E] and then 560 m [21 degrees E of N]. The entire motion takes 4.2 minutes.

a. what is the runners displacement?
b. what is the runners avg speed and avg velocity

a. using cosine law I get
delta d^2 = 850^2 + 560^2 - 2(850)(560)cos111
d = 1173 m

sin thetha / 560 = sin111 / 1173
thetha = 26 degrees

the runners displacement is 1173 m [31 degrees E of N]

b. avg speed = (850 + 560) / 252
= 6 m / s

avg velocity = 1173 / 252
= 4.7 m / s [31 degrees E of N]

Things look right to me, but my numbers are off a fair bit compared to the answers in the book. I would like for somebody to see if I have made any errors. Thanks

 

[soroban]

Hello, Clifford!

I believe your obtuse angle is off . . .

A runner runs in a straight line of 850 m [25° N of E]
and then 560 m [21° E of N]

                                              * C
                                            *
                                          *
                                        * 
                              :       *  560
                              : 21° *
                              :   *
                          90o : *
                  - - - - - - * B
                    25°   *
                      *
                  *
              *    850
          * 25°
    A * - - - - - - - - - - - - - - -

I found that: \(\displaystyle \,\angle ABC\:=\:21^o\,+\,90^o\,_\,25^o\:=\:136^o\)