The coordinate plane below shows the path of a bicyclist. Each square represents 10 meters. a. What is the displacement of the cyclist? (3 points) b. What is the distance traveled by the cyclist? (3 points) c. If the whole trip takes 45 seconds, what is the average speed of the cyclist? (3 points) d. If the whole trip takes 45 seconds, what is the average velocity of the cyclist? (4 points) e. Between points B and C, the cyclist decreases his speed from 4 m/s to 3 m/s in a time of 3 seconds. What is the magnitude of his acceleration? (4 points) You stand on a bridge above a river and drop a rock into the water below from a height of 35 m. (Assume no air resistance.) a. What is the acceleration of the rock as it falls? (3 points) b. How long does it take to hit the water? (4 points) c. How much more time would it take if instead of dropping the rock straight down, you threw it horizontally with a speed of 20 m/s? (6 points) d. You throw another rock at an angle of 65 above the horizontal with a speed of 20 m/s. What are the x- and ycomponents of the rock's speed? (4 points) e. How long does it take the rock to reach its maximum height? (3 points) Jane works at a grocery store. She has a large crate of bananas with a mass of 13 kg to move to the produce aisle. a. What is the weight of the crate? (2 points) b. What is the normal force acting on the crate when it sits on the floor? Explain how you found the answer. (2 points) 0. If she pushes on the box with a force of 40 N and there is no friction, what is the acceleration of the box? (2 points) cl. If the coefficient of static friction between the crate and the floor is 0.2, what is the maximum force of static friction acting on the crate? (2 points) e. If she pushes on the crate with a force of 12 N, what is the force of static friction acting on the crate? Explain how you found the answer. (3 points) f. If she pushes on the crate with a force of 40 N, and the coefficient of kinetic friction is 0.15, what is the net force on the crate in the X-direction? (3 points) g. Based on your answer in part (f), what is the acceleration of the crate? (3 points) Trigonometric functions: sin(0) = opp hyp cos(0) = adj hyp tan(0) = opp adj Kinetic energy: KE = _ mv2 Gravitational potential energy: GPE = mgh Acceleration due to gravity: g = 9.81 m/s2 Work: W = AKE Work: W = Fd Displacement: Ad = Last2 + v,At Final velocity: V2 = V1 + at Distance: d = vt Acceleration: a = 4v At Force: F = ma Normal force: FN = mg cos(0) Weight: w = mg Force of friction, kinetic: FK = HKFNForce of friction, static: Fs = HSFN Momentum: p = mv Impulse: I = Ap = FAt Elastic potential energy: EPE - _kx2 Gravitational force: F _ Gm,m2 Gravitational constant: G = 6.67 x 10-11 N . m2/kg2 Centripetal acceleration: a = ax2 + bx2 + c= 0 Quadratic equation: x=-b+vb2 -4ac 2a