1. Headbutting a Soccer Ball

Emery is practicing their soccer skills. They headbutt a soccer ball directly upwards with an initial velocity of 1.5 m/s. Qualitatively sketch the graphs listed below (i.e., do not include numbers on your graph) from the time Emery releases the ball upwards until immediately before they catch the ball.

a. Position versus time for the soccer ball

b. Velocity versus time for the soccer ball

c. Acceleration versus time for the soccer ball

2. Come Sail Away

A sailboat is sailing along the Long Island sound initially at 5.1 mph. The sailor raises the sails which catch the wind and the sailboat speeds up at a uniform rate. While speeding up, the sailboat travels through 8.2 miles. When the sailboat reaches a speed of 17 mph, the sailor pulls the sails back down so the sailboat moves at a constant velocity again. Please write your answers in SI units.

a. What is the sailboat's acceleration (magnitude and direction) when the sails are raised?

b. How much time does it take the sailboat to reach 17 mph?

c. After reaching 17 mph, how long will the sailboat have to travel to reach Long Island (which is 7.1 miles away)?

3. Position, Velocity, and Acceleration Graphs

Shown below is three different sets of position, velocity, and acceleration versus time graphs for three different physical situations. Each column represents a different physical situation. All the curved lines shown in the graphs below are quadratic. Fill in the empty graphs (inside the red boxes) to correspond with the other shown kinematic graphs. Each column of kinematic graphs should be consistent with one another for the same physical situation. Please show your work and/or explain your reasoning of how you filled in the graphs.

\fU 2 8 N = Vor + 2axAx U CC N = voy 2 + 2ay Ay