Extra Credit Problems You may attempt to do all Extra Credit Problems, but you may only get credit for one of these problems. Indicate the problem that would like me to grade for extra credit. X1) (5 points) If a and b are any two vectors, prove that (a - b) x (a + b) = 2(a x b). X2) (5 points) If a particle with mass m moves with position vector r(t), the its angular momentum is defined as L(t) = mr(t) x v(t) and its torque as t(t) = mr(t) x a(t). i) Prove that L' (t) = t(t). ii) Prove that if t(t) = 0 for all t, then L(t) is constant. ( The Law of Conservation of Angular Momentum) X3) A projectile is fired with an initial speed of 200 m/s and angle of elevation 60. The projectile is fired from a position 110 m above the ground. (Use g = 9.8 m/s2. Round your answers to the nearest whole number.) i) Find the range of the projectile. ii) Find the speed at impact