Problem 4-12 - Vector components - Part 4 - (C)

A car is travelling along a winding highway at a constant speed of \(82\; km/h.\) At 3:00 p.m., the car is heading \(38.2^\circ\) east of north, and at 3:15 p.m. it is heading \(12.7^\circ\) south of east. Define the \(+x\) and \(+y\) directions to be east and north, respectively. Use Eq. 4-8 to determine the \(x\)- and \(y\)-components of the average acceleration during this time interval.  

Accumulated Solution

\(82\; km/hr = 22.8\; m/s \\ v_{fx} = 22.8 \cos 12.7^\circ = 22.24\; m/s \\ v_{fy} = -22.8 \sin 12.7^\circ = -5.01 \;m/s\)

Vector coordinates v_i and v_f

Correct!

 

The \(x\) and \(y\) components of \(v_i\) are:

Solution \(x\) \(y\)
(A) \(22.8 \cos 38.2^\circ = 17.92\; m/s\) \(22.8 \sin 38.2^\circ = 14.10\; m/s\)
(B) \(22.8 \sin 38.2^\circ = 14.10\; m/s\) \(22.8 \cos 38.2^\circ = 17.92\; m/s\)
(C) \(-22.8 \sin 38.2^\circ = -14.10\; m/s\) \(22.8 \cos 38.2^\circ = 17.92\; m/s\)
(D) \(22.8 \cos 38.2^\circ = 17.92\; m/s\) \(-22.8 \sin 38.2^\circ = -14.10 \;m/s\)