An archer exerts an average horizontal force of 12N on a bow-arrow system while pulling the bow string with arrow back 0.30m from the resting point. If arrow’s mass is 0.45kg, what is the horizontal speed of the arrow when it leaves
the bow? [4.0m/s]

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Astone is thrown with a speed v0 and returns to earth, as the drawing shows. ignore friction and air resistance, and consider the initial and final locations of the stone. which one of the following correctly describes the change δpe in the gravitational potential energy and the change δke in the kinetic energy of the stone as it moves from its initial to its final location? options a.δpe = 0 j and δke = 0 j b.δpe is positive and δke is negative c.δpe = 0 j and δke is positive d.δpe is negative and δke is positive e.δpe = 0 j and δke is negative

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?