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Problems: 2D Constant Acceleration Kinematics

Assume that the acceleration is completely along the y-axis.

             

1. HRW 6, Q 4.7 In the figure, the path of a "cream tangerine" (i.e. ball) is shown as it moves up past windows A, B, and C that are identical in size and regularly spaced vertically. Rank the times needed to pass the windows starting with the window having the largest time. (Answers might be A=C>B for example.) Does the regular vertical spacing matter?

The tangerine now passes by windows D, E, F that are identical to each other and regularly spaced horizontally. Rank the times needed to pass the windows starting with the window having the largest time. Does the regular horizontal spacing matter?

2. I shoot a ball from a cannon at 15.0 m/s, 60degrees above the horizontal. It lands on a platform that is 8.0 m vertically above the end of the cannon. Find the horizontal distance from the end of the cannon to the point where the ball hits.

3. I throw a snowball from a roof 16.00 m high with a velocity of 15.00 m/s at some angle above the horizontal. The angle it is thrown at is (37° ± 2°). Assume free fall.

(a) Where does the ball land horizontally?

(b) What is the velocity of the ball as it hits? Give the answer using unit vectors and also as a magnitude and direction.

We want an idea of the uncertainty in the answers. Different groups should use different angles. Each table should do two of the three possible angles, 35deg, 37deg, and 39deg

4. HRW 33P An airplane has a speed of 290.0 km/hr and is diving at an angle of 30.0deg below the horizontal when the pilot releases a package of relief food. The food travels a horizontal distance of 700.0 m from its point of release to the point where it hits the ground, and we will assume "free-fall". (a) How long is the food in the air? (b) How high was the plane when it released the food?

5. You get the opportunity to play pro-basketball with Michael Jordan. The team is down by 2 points with time running out. Michael feeds you the ball and you take a shot with 0.82 seconds remaining. It goes in, with nothing but net, as the buzzer sounds! As with all your shots, the ball leaves your hands at a height of 6 ft (1.83 m) at an angle of 30 degrees from the horizontal. Does the game go into overtime or have you won? (You also need to know that (1) a three point shot must be thrown from a distance of more than 7.239m from the basket; (2) the height of the basketball rim is 3.048 m).

6. A 2002 commercial showed a Kia driver trying to jump a chasm. The car drove off the left portion of a bridge that was angled at 8? above the horizontal, and just missed the right portion of the bridge located a distance W = 6.0 m away. Instead the car crashed at the base of the chasm, at H = 8.0 m below the receiving bridge. Assume you were hired to stage this stunt. For safety reasons you want the right bridge abutment to just pass above the windshield of the car. You must tell the stunt driver how fast to drive (in miles per hour!) when he leaves the bridge, and you want to know the speed of the car (in miles per hour!) when it crashes into the base of the chasm. The props department also needs to know how long the receiving bridge must jut out past the crash point.