Horizontal Projectiles

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

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!

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

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

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)

= 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

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

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

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?

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?

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?