A yo-yo is attached to the end of a string. A professional yo yo is spinning it by the string around in a circular motion. All of a sudden he lets go of the string. What direction is the yo yo moving in initially?

The force will determine the acceleration.

Askydiver weighing 140 lb (including equipment) falls vertically downward from an altitude of 19,000 ft and opens the parachute after 18 s of free fall. assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.55|v| when the parachute is closed and is of magnitude 14|v| when the parachute is open, where the velocity v is measured in ft/s. assume that acceleration due to gravity has magnitude 32 ft/s/s; remember that weight is the product of mass and gravitational acceleration. (a) find the speed of the skydiver when the parachute opens. (b) find the distance fallen before the parachute opens. (c) what is the limiting velocity vl after the parachute opens? (d) determine how long the sky diver is in the air after the parachute opens. (e) plot the graph of velocity versus time from the beginning of the fall until the skydiver reaches the ground.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒