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vectors-and-relative-velocity

A train is heading east at 60 mi/hr. A car approaches the track crossing heading northeas~- at 45 mi/hr on a road that makes a 55° angle with the track. See Figure 2.3-3. Whatis-the velocity of the train relative to the car? What is the speed of the train relative.tethe car?

figure 2.3-3/

Solution

• Solution
Velocity is a vector quantity consisting of speed and direction. Speed is the magnitude of the velocity vector. The train’s velocity VR relative to the car is the difference between the train’s velocity·vT relative to the ‘ground and the car’s velocity Vc relative to the ground. Thus
VR = VT – Vc Choosing the x direction to be east, and the y direction north, we can write the following
velocity vectors: .1
VT = 6Oi+OJ Vc =45 os (55°)i + 45 sin(55°)j
In MATLAB we can write these vectors as follows (remembering to convert 55° to radians)
and compute VR »v_T = (60….—01;
»v_c =>—[f5*cos{55*pi/180), 45*sin{55*pi/180)); >i = V_T-V_C .
//-V.:..R 34.1891 -36.8618

Thus VR = 34.189li – 36.8618j miI hr. The velocity of the train relative to the car is approximately 34 mi/hr to the  ast and 37 miI hr to the south. The relative speed SR is the magnitude Of VR. which can be found as
SR = J(34.1891)2 +(-36.8618)2 = 50.2761 miI hr In MATLAB the speed can be calculated as follows: »s_R = sqrt (v_R(l A2+v_R(2)A2) We will soon see an easier y to compute SR using array multiplication.