#1: Two vectors are expressed in terms of their components as follows:
Ax = 2.0 units
Ay = 8.0 units
Bx = 4.0 units
By = -2.0 units
1. Find the dot product, A \cdot B, of the two vectors. 2.
2. Find the angle $\theta$ between the two vectors, in degrees.
#2: A person is riding a skateboard, traveling 80 m in the x-direction. The person is being pulled by a rope that is
tied to a bicyclist; the force exerted by the rope is given by:
$\vec{F} = 17\hat{x} + 12\hat{y}$
1. Find the total work done on the skateboarder by this force during their motion.
#3: A 70-kg skier is traveling horizontally along a (frictionless) snow-covered plain, when he encounters a rough
patch. The coefficient of friction between the skier and the ground in the rough patch is given by:
$\mu_k = 2x + 8x^2 - 24x^3$
where x is measured from the beginning of the friction patch, which is 0.5 m long.
1. Find the total work done on the skier by the friction patch.
