1. Horizontal Projectiles

3. Which ball hits the ground first?
Red ball
Yellow ball
Both hit at the same time

4. Horizontal (x) motion and vertical (y) motion
are independent!
x-motion = constant velocity
y-motion =
free-fall
This is an example of: Projectile Motion
Any 2-dimensional problem =
Two 1-dimensional problems
Solve them separately!

5. Use kinematic equations
Key Concepts:
ax= 0
ay= -g
Vx = x/tair
Use kinematic equations

7. 1. A cannonball is projected horizontally with an initial velocity of 120 m/s from the top of a cliff 250 m above a lake.
a. In what time will it strike the water at the foot of the cliff?
vx = 120 m/s
y = 250 m
vy = 0
= 7.14 s
b. What is the x-distance (range) from the foot of the cliff to the point of impact in the lake?
x = vx t
= 120(7.14)
= 857 m

8. vx = 120 m/s vy = voy + gt = 9.8(7.14) = 70 m/s = 139 m/s
c. What are the horizontal and vertical components of its final velocity?
vx = 120 m/s
vy = voy + gt
= 9.8(7.14)
= 70 m/s
d. What is the final velocity at the point of impact and its direction?
= 139 m/s
= 30.2 below horizontal
v (139 m/s, 30.2)

9. = 7.14 s x = vx t = (80)(7.14) = 571 m vx = 80 m/s vy = gt
2. An airplane traveling at 80 m/s at an elevation of 250 m drops a box of supplies to skiers stranded in a snowstorm.
a. At what horizontal distance from the skiers should the supplies be dropped?
vx = 80 m/s
y = 250 m
= 7.14 s
x = vx t
= (80)(7.14)
= 571 m
b. Find the magnitude of the velocity of the box as it reaches the ground.
vx = 80 m/s
vy = gt
= (9.8)(7.14)
= 70 m/s
= 106 m/s

10. 3. A person standing on a cliff throws a stone with a horizontal velocity of 15.0 m/s and the stone hits the ground 47 m from the base of the cliff. How high is the cliff?
vx = 15 m/s
x = 47 m
vy = 0
= 3.13 s
y = ½ gt2
= ½ (9.8)(3.13)2
= 48 m

11. Can you predict the impact point of a projectile launched from the edge of the table with horizontal velocity?

12. Horizontal Example Problem
A rifle is aimed horizontally at a target 30 m away. The bullet hits the target 1.9 cm below the aiming point.
What is the bullets time of flight
What is the bullets speed as it emerges from the rifle?

13. Ex: If you throw a dart horizontally at 30 m/s toward a target 2
Ex: If you throw a dart horizontally at 30 m/s toward a target 2.0 m away, how far below your aiming point will it hit?

14. If someone foolishly tries to run horizontally off the roof of a 12 m tall hotel and land in the pool, how fast must they run if the pool is 3 m from the base of the hotel?