1. Chapter 7
Projectile Motion

2. Projectile Motion
The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.

3. Projectile Motion
Because we ignore air resistance, the only force acting on thrown objects is gravity.

4. Projectile
The object that has been given an initial thrust, fired, or thrown into air.

5. The path of a projectile as it travels through space.
Trajectory
The path of a projectile as it travels through space.

6. In Projectile Motion
The vertical & horizontal components act independently & can be solved independently

7. In Projectile Motion
The only force acting vertically is the force of gravity causing downward acceleration.

8. In Projectile Motion
There are no net forces acting horizontally; thus, the horizontal velocity is constant.

9. In Projectile Motion
Use your velocity formulas to solve for vertical & horizontal motion independently.

10. In Projectile Motion Solve for time in air 1st
Always use the vertical component to solve for the time in air.

11. In Projectile Motion
After solving for the time in air, solve for the range or horizontal distanced traveled

12. A rock has been thrown horizontally at 4. 0 m/s from a tower 49 m high
A rock has been thrown horizontally at 4.0 m/s from a tower 49 m high. Calculate: tair, dH, and vH & vV the instant before impact:

13. A plane flying horizontally at 250 m/s at an altitude of 4
A plane flying horizontally at 250 m/s at an altitude of 4.9 km high drops a bomb. Calculate: tair, dH, and vV the instant before impact:

14. Drill: A ball rolls at 75 cm/s off the edge of a 49 cm table
Drill: A ball rolls at 75 cm/s off the edge of a 49 cm table. Calculate: tair, maximum vV,
and dH:

15. A car traveling at 1500 cm/s goes off the edge of a 0.49 km high cliff. Calculate: tair, dH, and maximum vV:

16. A car accelerates at 5.0 m/s2 for 250 m before going off the edge of a 0.49 km high cliff. Calculate: t & max v on the ground, & t, dH, and max vV in air:

17. Drill: A bullet exits a 0. 50 m barrel horizontally at 500
Drill: A bullet exits a 0.50 m barrel horizontally at m/s from a height of 2.0 m. Calculate: (a & t)in barrel, (t, max vV, & dH)in air:

18. A cannon ball is fired at 1000. 0 m/s at 53o from horizontal
A cannon ball is fired at m/s at 53o from horizontal. Calculate: max height, tair ,vV at impact, dH:

19. Repeat the last problem with a cannon ball exiting the barrel at the same speed with angles of 40o, 45o, & 50o

20. Assumming all factors are the same for that cannon, Calculate its maximum range:

21. Drill: A ball is thrown at 25 m/s at 45o from horizontal. Calculate:
tair, hmax, vV max, dH:

22. A ball is thrown at 25 m/s at 53o from horizontal
A ball is thrown at 25 m/s at 53o from horizontal. Calculate: vV, vH, tair, hmax, & dH

23. A 25 Mg car is accelerated from rest at 5
A 25 Mg car is accelerated from rest at 5.0 m/s2 up a 250 m ramp at 37o from horizontal. Calculate: t, & vf on the ramp, and dV, dH, t, and maximum vV in air:

24. A 1. 0 Mg block slides from rest down a 250 m ramp (m = 0
A 1.0 Mg block slides from rest down a 250 m ramp (m = 0.20) at 37o from horizontal that ends 490 m above the ground. Calculate: t, & vf on the ramp, and dH, t, and maximum vV in air:

25. Review

26. A sled coasts off a 0.49 km cliff at 18 km /hr.
Calculate: tair, max vV, & dH:

27. A catapult launches a 250 kg rock at 100. 0 m/s at 37o from horizontal
A catapult launches a 250 kg rock at m/s at 37o from horizontal. Calculate: tup, dV, tair, & dH :

28. Define each of the following
Distance Displacement
Speed Force
Velocity Acceleration

29. Give Units for each of the following
Distance Displacement
Speed Acceleration
Velocity Force

30. vf = vi + at
d = vit + ½ at2
vf2 = vi2+ 2ad

31. Projectile Motion Projectile Trajectory

32. A 25 Mg sled slides from rest down a 500. 0 m slope (m = 0
A 25 Mg sled slides from rest down a m slope (m = 0.10) at 37o from horizontal that ends 2.45 km above the ground. Calculate: t, & vf on the slope, and dH, tair, and the maximum vV in air:

33. A 250 Mg sled accelerates at 3. 0 m/s2 up a 250 m ramp (m = 0
A 250 Mg sled accelerates at 3.0 m/s2 up a 250 m ramp (m = 0.25) at 53o from horizontal. Calculate: Fa, tramp, vf ramp, tair, dv, & dH

34. A 0. 10 Mg cycle is accelerated with a force of 500. 0 N for 10
A 0.10 Mg cycle is accelerated with a force of N for 10.0 s before hitting a 25 m ramp at 37o from horizontal. Draw the system and Calculate: v at bottom & top of ramp, and t, dv, & dH in the air

35. An airplane is flying horizontally due west at 360 km/hr at an altitude of 0.49 km & drops a 2000 lb bomb. Draw the system and Calculate: tair, maximum vV, & dH.

36. A 50. 0 kg person skis (m = 0. 010) down a 3
A 50.0 kg person skis (m = 0.010) down a 3.0 km ski trail with an average slope of 30o. Draw the system and Calculate: a, t, maximum v on the trail

37. British Ships had cannons with muzzle velocities of 400 m/s while the cannons at Ft McHenry could fire at 500 m/s. The British could elevate to 45o while the Americans could elevate to 18o. Which cannons had the greater range.

38. Expanding gases produce about 10,000 N of force in a gun barrel
Expanding gases produce about 10,000 N of force in a gun barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/s2.

39. a b A B
a = 37o
= 53o
Y = 1.00 kN C X Y

40. A B C Wx + WY FV of C a b FV of A FV of B + FV of C FH of A FH of C
FH of B C
FH of C
Wx +
FV of C WY

41. A B C Wx + WY FV of C a b FV of A FV of B FH of A FH of C FH of B

42. A 200. 0 kg rock is catapulted at 53o from horizontal at about 0
A kg rock is catapulted at 53o from horizontal at about 0.10 km/s. Draw the system and Calculate: t, dv, & dH in the air

43. A rock is thrown at 37o from horizontal at about 25 m/s
A rock is thrown at 37o from horizontal at about 25 m/s. Draw the system and Calculate: t, dv, & dH in the air