Homework Problems - Projectile Motion

Once you recognize a situation as a projectile motion problem, proceed with this strategy:
1) Draw a picture;
2) Install an x-y coordinate system with the origin at he point of projection;
3) determine to the extent you can the x-y address of some important point;
4) select the appropriate equation from page three.
Solutions to the odd-numbered problems appear at the bottom of this page. Consult your table mates to check your solutions to the other problems.

1. A book slides across a table top at 3 m/s and onto the floor .8 m below. a) How far from the base of the table did the book land? b) How long was it airborne? c) How long would it take a similar book dropped from the same height to hit the floor? solution

2. A soccer player kicks a ball at 25 m/s at an angle of 37 degrees above the ground. a) Where does the ball land? b) How long is it in the air?

3. A ball rolls off a table top 1.2 m high and lands 4 m from the base of the table. a) How long is the ball in the air? b) With what speed did it leave the table top? c) What are the horizontal and vertical components of the velocity of the ball as it hits the ground?solution

4. A cannon is mounted on a plateau 50 m above a level plain. A shell is fired at a speed of 200 m/s at an angle of 40o above the horizontal. a) Where does the shell land? b) How long is it airborne? c) What are the horizontal and vertical components of the velocity when the shell hits the ground?

5. 5. . An airplane is flying in level flight at an altitude of 200 m and with a speed of 70 m/s. The pilot wishes to drop a mail sack to some campers on the ground. At what horizontal distance from the campers should the mail pouch be released so that it lands amidst the campers? Show also the location of the plane when the pouch lands.

6. A ball rolls off a table 1 m high and lands 2 m from the base of the table. a) With what speed did the ball leave the table? b) How long was it airborne? c) Determine the horizontal and vertical components of the velocity as the ball hits t he floor. d)Determine the vector sum of these velocities.

7. In a baseball game, the batter hits a ball from a height 3 ft off the ground. The ball leaves the bat at 45o traveling at 110 ft./s and is headed for the left field fence 24 ft high and 320 feet away. Is the ball a home run? Note: use g = -32 ft/s2

8 . An airplane swoops down to drop supplies to hikers marooned by a storm. The plane is cruising at 200 km/hr in level flight and drops a package from an altitude of 150 m. a) Where must the package be released if it is to land in the midst of the hikers? b) Where is the plane when the package hits the ground?

9. A ball rolling at 5 ft/s rolls off a level landing and over a set of stairs where the treads are 8 inches wide and the risers are 8 inches deep. Which step does the ball hit first?

10. At a world cup soccer match, Polish superstar, Vaclav [friends use his middle name, acla] Zbrkzknsky, kicks the ball at an angle of 37o with a speed of 35 m/s. a) How long is the ball airborne? b) Where does the ball land? c) What maximum height did the ball attain above the ground?

11. A golfer, Kitty Deforest, (don't call me Eldrick) playing in the member/guest tournament at the Never Metric CC prepares to hit a tee shot
toward a green that is elevated 24 feet above the level of the tee. The hole plays as a par 3, with the center of the circular (R = 17 yds) green 142 yds from the tee. She can hit the ball consistently at 45 degrees above the horizontal. For what range of launch velocities will the ball strike the green?

 1.a) x = 1.21 m --b) t = .4s --c) t = .4s 7.Hint. It's a home run if x = 320 ft. Find y 3. a) t = .49 s ---b) Vo = 8.08 m/s ---c) Vx = 8.08 m/s -------Vy = -4.8 m/s 9 Hint: Solve by trial & error. Let y = -2/3 ft, find x 5. x = 447 m