Question 1: Pool players often pride themselves on their ability to impart a large speed to a pool ball. In the sport of billiards, event organizers often remove one of the rails on a pool table to allow players to measure the speed of their break shots (the opening shot of a game in which the player strikes a ball with his pool cue). With the rail removed, a ball can fly off the table. As the only participant with a physics background, they have placed you in charge of determining the speed of the players' break shots.

The top of the pool table is 0.870 m from the floor. The placement of the tape is such that 0 m is aligned with the edge of the table (as shown). The winner of the competition wants to know if he has broken the world record for the break shot of 32 mph (about 14.3 mis). If the winner's ball landed a distance 4.55 m from the table edge, calculate his break shot speed.

At what speed did his pool ball hit the ground?

Question 2: A speedboat moves on a lake with initial velocity vector v_1,x = 9.43 m/s and v_1,y = -2.41 m/s, then accelerates for 5.31 seconds at an average acceleration of a_avx = -0.107 m/s² and a_avy = 0.103 m/s². What are the components of the speedboat's final velocity, v_2,x and v_2,y?

Find the speedboat's final speed.

Question 3:

Emmy kicks a soccer ball up at an angle of 45° over a level field. She watches the ball's trajectory and notices that It lands, two seconds after being kicked, about 20 m away to the north. Assume that air resistance Is negligable, and plot the horizontal and vertical components of the ball's velocity as a function of time. Consider only the time that the ball is In the air, after being kicked but before landing. Take "north" and "up" as the positive x and y directions, respectively, and use g =10 m/s² for the downward acceleration due to gravity.

Question 4:

An airplane releases a ball as it flies parallel to the ground at a height of 165 m as shown in the figure. If the ball lands on the ground exactly 165 m from the release point, calculate the speed v of the plane.

Neglect any effects due to air resistance, and use g = 9.81 m/s² for the acceleration due to gravity.

Question 5:

You would like to shoot an orange in a tree with your bow and arrow. The orange is hanging 5.00 m above the ground. On your first try, you fire the arrow at 34.0 m/s at an angle of 30.0° above the horizontal from a height of 1.20 m while standing 52.0 m away. Treating the arrow as a point projectile and neglecting air resistance, what is the height of the arrow once it has traveled the 52.0 m horizontally to the tree?

If you fire at the same speed and angle on your second try, how far away could you stand such that the arrow will hit the orange?

Assume that the orange remains fixed in place during the arrow's flight. Select all that apply.

87.2 m

95.0 m

59.8 m

14.9 m

7.1 m