Simple Nature - Light and Matter

Incorrect solution #4:(same notation as above)Incorrect solution #5:(same notation as above)A x = (5.0 km) cos 45 ◦ = 3.5 kmB x = −(12.0 km) cos 55 ◦ = −6.9 kmA y = (5.0 km) sin 45 ◦ = 3.5 kmB y = −(12.0 km) sin 55 ◦ = −9.8 kmC x = A x + B x= −3.4 kmC y = A y + B y= −6.3 km√|C| = Cx 2 + Cy2= 7.2 kmdirection = tan −1 (−6.3/ − 3.4)= 62 ◦ north of eastA x = (5.0 km) cos 45 ◦ = 3.5 kmB x = −(12.0 km) sin 55 ◦ = −9.8 kmA y = (5.0 km) sin 45 ◦ = 3.5 kmB y = −(12.0 km) cos 55 ◦ = −6.9 kmC x = A x + B x= −6.3 kmC y = A y + B y= −3.4 km√|C| = Cx 2 + Cy2= 7.2 kmdirection = tan −1 (−3.4/ − 6.3)= 28 ◦ north of east3.4.4 Calculus with vectorsy / Visualizing the accelerationvector.DifferentiationIn one dimension, we define the velocity as the derivative of theposition with respect to time, and we can think of the derivative aswhat we get when we calculate ∆x/∆t for very short time intervals.The quantity ∆x = x f − x i is calculated by subtraction. In threedimensions, x becomes r, and the ∆r vector is calculated by vectorsubtraction, ∆r = r f − r i . Vector subtraction is defined componentby component, so when we take the derivative of a vector, this meanswe end up taking the derivative component by component,v x = dxdt ,v y = dydt ,v z = dzdt208 Chapter 3 Conservation of Momentum