Asoccer player practices kicking the ball into the goal from halfway down the soccer field. the time it takes for the ball to get to the goal from the time it is kicked averages about three seconds. the soccer field is 90 meters long. the player wants to know the average velocity of the ball. is there enough information to calculate this?

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.

Suppose that 27 j of work is needed to stretch a spring from its natural length of 6 m to a length of 9 m. (a) how much work is needed to stretch the spring from 12 m to 14 m? j (b) how far beyond its natural length will a force of 78 n keep the spring stretched?

An object with initial temperature 130 ∘ f is submerged in large tank of water whose temperature is 50 ∘ f . find a formula for f ( t ) , the temperature of the object after t minutes, if the cooling constant is k = − 0.2 . remember newton's law of cooling (the rate of change of temperature with respect to time is equal to k times the difference between the temperature of the object and the surrounding temperature) ! : )