PROJECTILE MOTION: In-Class Example Problems

ANGLED PROJECTILES: In-class example problems Q-AA

Q) A cannon fires a cannonball at an angle of 30 o above the horizontal. The ball leaves the cannon at 40 m/s. Find:

a. the horizontal component of the initial velocity. b. the vertical component of the initial velocity. c. the maximum height reached. d. the total flight time (assuming that it is fired and lands at the same elevation). e. the range of the cannon. f. the impact velocity of the cannonball.

R) How fast must a cannonball be shot out of the cannon if its angle of elevation is 20o above the horizontal and it must hit a target 100 m away (at the same elevation as the end of the cannon)? How long will it take to hit the target?

S) At what times will the cannonball from the previous problem be at a height of 3 m above the ground?

T) A projectile is fired with a velocity of v at an angle of  above the horizontal. Using only variables, derive an equation (in terms of v, , and g) for:

i) the maximum height attained. ii) the range of the cannon.

U) Find the range of a projectile that is fired at a speed of 80 m/s at an angle of ….

i) 25o ii) 35o iii) 45o iv) 55o v) 65o

When does the maximum range occur? Explain your results by referring to the components of the initial velocity in each case.

V) A projectile is fired at a speed of 60 m/s and an angle of 30o above the horizontal from the top of a 100 m tall building. Find:

ii) the horizontal distance away from the building that the projectile lands. iii) the total flight time of the projectile.

W) A projectile is fired at a speed of 60 m/s and at an angle of 30o below the horizontal from the top of a 100 m tall building. Find:

iv) the horizontal distance away from the building that the projectile lands. v) the total flight time of the projectile. X) If a projectile is fired at a speed of 50 m/s at an angle of 45o above the horizontal, track the projectile’s …..

vi) position at t = 1, 2, & 3 seconds. vii) velocity at t = 1, 2, & 3 seconds.

Y) A field goal kicker is kicking a field goal from 50 yards away (from the 10 ft tall goal post). The ball is kicked at an angle of 25o and a speed of 70 mph. If the ball is kicked straight at the field goal post, will it clear bottom bar? If so (or if not), by how much would it (or would it not) clear? (remember: g = -32.2 ft/s2, 1 yd = 3ft, 1 mi = 5,280 ft, 1 h = 3600 sec)

Z) Would the ball in the previous problem have been on its way up or on its way down when reached the field goal post? Logically explain how you can tell.

AA) A ball kicked off the top of a 30 m tall building. It is kicked at an angle of 20o above the horizontal with a speed of 20 m/s. Find:

i. the horizontal distance away from the building that the ball will land. ii. the time that the ball will take to reach the ground. iii. the maximum height off the ground attained by the ball. Projectile Motion (at an angle) Problems Day #5 HW

22. A golf ball is hit from level ground at an angle of 60o above the ground with an initial speed of 40 m/s. Determine the (a) horizontal range and maximum height of the ball.

23. A cannon ball is fired (assume from ground level) at a speed of 1200 m/s with an angle of 30o above the ground. Determine (a) the maximum height and (b) horizontal range of the cannon ball.

24. On level ground, a ball is thrown forward and upward. The ball is in the air 2 sec, and strikes the ground 30 m from the thrower. With what speed and at what angle was the ball thrown? Assume that the ball is thrown and caught at the same height.

25. A broad jumper takes off at an angle of 20o above the horizontal and jumps 0.60 m high.

(This is  ymax )

a. What is her forward velocity? b. How far does she jump?

26. A ball is fired with a velocity of 1700 m/s at an angle of 55o above the horizon. Determine (a) the ball’s horizontal range, (b) the amount of time that the ball is in motion?

Day #6 HW 27. A ball is launched off the top of a 30 meter tall building with a speed of 20 m/s at an angle of 30o above the horizontal. Find the ball’s …

a) max height reached (above the ground). b) total flight time. c) max range. d) impact velocity.

28. A ball is launched off the top of a 30 meter tall building with an unknown speed at an angle of 40o above the horizontal. The ball reaches a maximum height of 50 meters above the ground. Find the ball’s …

a) initial speed. b) total flight time. c) landing distance away from the building.

29. A ball is rolled off the building from problem #28 above. It rolls off horizontally at an unknown speed and lands 15 meters from the building. Find its initial speed and its impact velocity.

30. A tank fires a large bullet at a speed of 100 m/s. It leaves the barrel at an angle of 40o. There is a very dense fog that is hovering 20 m above the ground. Find the times (after firing) that the bullet will enter and exit the fog layer.

31. A baseball player hits a fly ball to a height of 50.0 m. After the bat strikes the ball, how much time does a fielder have to get into position to make the catch? Day #7 HW

32. A ball is thrown off of a 100 m cliff with a velocity of 25 m/s at an angle of 600 above the horizon. What is the ball’s (a) max height, (b) horizontal range, (c) impact velocity?

33. A golf ball is hit with an initial angle of 34o with the horizontal and lands exactly 240 m down range on level ground. (a) What was the initial speed of the ball, (b) the maximum height of the ball?

34. A pilot cuts loose two of his fuel tanks in an effort to gain altitude. At the time of release, he was 120 m above the ground and traveling upward at an angle of 30o above the horizontal, with a speed of 84 m/sec. For how long were the tanks in the air?

35. A daredevil is shot out of a cannon at 45o to the horizon with an initial speed of 25.0 m/s. A net is placed 50 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil?

36. A place-kicker must kick a football from a point 36.0 meters from the field goal post. The ball must clear the crossbar, which is 3.05 meters high. When kicked, the ball leaves at 20.0 m/s at an angle of 53o above the horizon. (a) By how much does the ball clear the bar? (b) Was the ball on the way up or down when it went through?