Your medieval history class is constructing a trebuchet, a catapultlike weapon for hurling stones at enemy castles. the plan is to launch stones off a 71- m -high cliff, with initial speed 39 m/s . some members of the class think a 45 ∘ launch angle will give the maximum range, but others claim the cliff height makes a difference. what do you give for the angle that will maximize the range?

An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 127 ft at an angle of 31.0° above the horizontal. it then moves 127 ft at an angle of 46.0° 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.)

If vx = 7.00 units and vy = -7.60 units, determine the magnitude of v⃗ . determine the direction of v⃗ .

At a certain instant after jumping from the airplane a, a skydiver b is in the position shown and has reached a terminal (constant) speed vb = 52 m/s. the airplane has the same constant speed va = 52 m/s, and after a period of level flight is just beginning to follow the circular path shown of radius ρa = 2330 m. (a) determine the velocity and acceleration of the airplane relative to the skydiver. (b) determine the time rate of change of the speed vr of the airplane and the radius of curvature ρr of its path, both as observed by the nonrotating skydiver.