1. The problem statement, all variables and given/known data I have attached the problem. A 14,000 kg tractor traveling north at 21 km/h turns west and travels 26 km/h. Calculate the change in the tractor's a. kinetic energy b. linear momentum (magnitude AND direction) 2. Relevant equations delta KE = (1/2)mv^2 - (1/2)mvi^2 change in linear momentum (delta p) = m(vf-vi) 3. The attempt at a solution I defined east as positive and north as positive. I first converted the velocities to m/s to get: 5.83 m/s North and -7.22 m/s West. a) I used: delta KE = (1/2)mv^2 - (1/2)mvi^2 Since kinetic energy is a scalar quantity, I do not have to worry about direction. So... I will just plug in the values all given to find the change in KE. (1/2)(14000)(-7.22)^2 - (1/2)(14000)(5.83)^2 After computing I get 1.27*10^5 J --> Can anyone verify? b) This part is where I get lost... The change in linear momentum is the same thing as impulse. Impulse is m(vf-vi) --> I know I cannot just subtract the velocities that are given because they are not in same direction. They have direction and magnitude. I must use vectors to find the vf-vi. In vector notation, vf-vi is that same things as saying vf+(-vi) Turns out that the initial velocity only has a y component, which makes its velocity (after computing with the vectors) = 5.83 m/s The final velocity only has an x component and a 0 y component, which makes its velocity ( after computing with a y and x component) = -7.22 m/s After getting this far, if I did it right, I assume that now I must do another vector problem with the vector final + (- vector initial) I draw the final vector in the negative direction (west) and lable it with -7.22, then I flip the direction of the north vector (v initial) making it south to subtract from the v final. I get a vector pointing west, plus a vector pointing south. I draw an arrow from the tail of first to tip of last. I then have a right angle, do pythagorean theroem to find 86.1173 = resultant^2 ... I take the square root to get 9.27 Is this value vf-vi? If so, I multiply this by the mass of the truck to get the change in momentum? So..... (9.27) * 14000 kg = 1.30*10 ^5 kg*m/s To get the direction, I do the arctan of what values? Is it the velocity of final/intial?? Thanks for the help!