Angled Projectile Motion Problems

Name______Period______

Angled Projectile Motion Problems (HS1.6.4, HS5.1.1.4, HS5.1.1.6, HS5.1.2.6, HS5.1.2.C, HS5.1.1.3, HS1.4.1

Directions: Use the dual-column data list method to solve the following projectile motion problems:

Example: A hungry coyote is shot out of a cannon with an initial speed of 50 m/s at an angle of 60 degrees from the horizontal. He returns to the ground at the same level from which he started. a. For how much time will the coyote be airborne? b. How far will the coyote go in the horizontal direction? c. What is the highest elevation above the ground that the coyote reaches?

Data List: Solution:

x y h a) a = (vf - vo)/t d ? 0 m ? t = (-43.3 – 43.3)/-9.8 t ½ t total t = 8.84 sec. o o o vo 50 m/s cos 60 50m/s sin 60 50m/s sin 60 50 m/s cos 60o - 50m/s sin 60o 0 m/s vf b) dx = vot 0 m/s2 -9.8 m/s2 -9.8 m/s2 o a dx = 50cos60 (8.84sec) dx = 25m/s(8.84 sec) dx = 221 m The horizontal and vertical components of the 50 m/s velocity vector need to be found first, since the 50 m/s initial speed is not entirely in c) Since the highest point occurs at the either the x or y directions. midpoint of the flight path, only ½ the total flight time is used. Also, vfy at that point o vox = (50 m/s) cos 60 = 25m/s would be zero. o voy = (50 m/s) sin 60 = 43.4 m/s. d =( vfy + voy)t /2 d = (0 + 50 sin60o)( 4.42 sec)/ 2 d = (43.3m/s)(4.42s) /2 d = 95.7 m

1. The punter on a football team tries to kick a football so that it stays in the air for a long “hang time”. If the ball is kicked with an initial velocity of 25 m/s at an angle of 60o above the ground, a. Calculate the “hang time”. 4.42 sec. b. How far does the ball go in the horizontal direction? 55.25 m c. What is the maximum altitude (height) the ball reaches? 23.9 m

2. A hunter is practicing hitting a target that is down range. If the arrow leaves the bow at a velocity of 30 m/s at an angle of 40 degrees above the horizontal, 3.93 sec a. Calculate how much time it takes for the arrow to return to the bow level. 91 m b. Find out how far down range the arrow goes. 19 m c. What is the maximum altitude the arrow reaches?

3. A ball is thrown at a launching angle of 52o above the horizontal from one meter above the ground, with a velocity of 18 m/s. 10.3 m a. What is the highest barrier the ball can clear? 32.08 m b. How far will the ball go before being caught one meter above the ground? 2.89 sec c. How much time does it take for the ball to get to the catcher?

4. Another ball is struck by a batter at an angle of 30o and leaves the bat at a speed t = 4.08 sec of 40 m/s at a distance of one meter above the ground. How fast and in what dx = 141.4 m direction should an outfielder who is standing 120 meters away run in order d = 21.4 m to catch the ball at the same height it left the bat? v = 5.24 m/s

5. While trying to make some extra money to order more supplies from the 69o Acme supply catalog, a hungry coyote hires himself out to a circus to be the bullet in a cannon stunt. The cannon is capable of only one speed….30m/s… but its angle can be adjusted. The circus master tells the coyote that he better not tear through the tent roof again (its 40 meters above), so the coyote adjusts the cannon to what elevation above the horizontal?

o 6. In yet another escapade, the coyote launches himself at an angle of 40 across 48.7 m/s a field to land into a net a distance away. He must clear a 50 meter tall wall positioned in the center of the field. With what speed should he launch himself in order to just make it to the net?

7. Another stunt has the coyote riding a motorcycle up a 25o incline in order to jump 16 m/s a canyon of width 20 meters.What minimum speed must he have in order to just make it to the other side, touching down at the same level?

o 8. A bored kid, 30 meters from a building, throws a ball at an angle of 50 with a 9.07 m velocity of 20 m/s at the building wall. At what height above the throwing level will the ball hit the wall?

9. In an unfortunate skiing mishap, the coyote accidentally launches himself off a rather large ski slope at an angle of 50 degrees above the horizontal with a velocity of 100 m/s. He lands further down the slope, 250 meters below his original elevation. a. How far did he travel horizontally during this maneuver? 1184 m b. How high did he go above his landing point? 549.4 m