Chapter 3: Curvilinear Motion Uniform Circular Motion Chapter 3: Curvilinear Motion

Projectile - any body with initial velocity that follows a path called trajectory.

Equation for Projectile Motion S – Displacement Vo – Initial Velocity a – acceleration V – Final Velocity t – time elapsed

Example 1: (a) What was its initial speed? A football, kicked at an angle of 40ᵒ above the ground, reaches a horizontal range of 190 ft. (a) What was its initial speed? (b) What was its maximum height? (c) What was its time of flight?

Example 2: (a) What was the time of flight of the ball? A boy, upon seeing a ball on the ground, kicked it at a certain angle ɵ with the horizontal. The ball reached the highest point of its trajectory 2.50 sec after it was kicked, and traveled a horizontal distance of 120m before hitting the ground. (a) What was the time of flight of the ball? (b) What was ɵ the angle of firing of the ball? (c) With what speed did the ball hit the ground?

Example 3: (a) What was the initial velocity of the ball? In one of the UAAP games, a player released the ball 7 ft above the ground when he was 17 ft away horizontally from the basket. The basket is 10 ft above the ground. The ball sank in the basket after 0.7 sec. Neglecting air resistance: (a) What was the initial velocity of the ball? (b) What was the angle of firing of the ball? (c) With what speed did the ball sank in the basket?

Example 4: (a) With what speed was it thrown? A stone is thrown at an angle 300 above the horizontal from a windowsill that is 600 m above the ground. If it reached the highest point 8 seconds later. (a) With what speed was it thrown? (b) How high above the ground did it rise? (c) Where was it 4 sec and 12 sec after it was thrown? (d) With what speed did it strike the ground?

Example 5: An archer shoots an arrow with a velocity of 30 m/s at an angle of 20ᵒ with respect to the horizontal. An assistant standing on the level ground 30 m downrange from the launch point throws an apple straight up with the minimum initial speed necessary to meet the path of the arrow. What is the initial speed of the apple and at what time after the arrow is launched should the apple be thrown so that arrow hits the apple?

Example 6: A swimmer dived off a cliff with a running horizontal leap. What must his minimum speed be just as he leaves the top of the cliff so that he will miss the ledge at the bottom which is 2 m wide and 9 m below the top of the cliff?

Example 7: The car shown is just to clear the water-filled gap. Find the take off velocity. 6m 300 5.5 m

Example 8: A ball is thrown so that it just clears a 5 meters fence 18 meters away. If it left the hand 1.5 meters above the ground and at an angle of 600 with the horizontal, what was the initial velocity of the ball? 600 5 m 18 m

Example 9: A stunt man is to drive a car across the water-filled gap shown. Determine the car’s minimum take velocity, landing velocity and the angle θ of the landing ramp. V 3m A 1 2 12 m

Example 10: will strike the incline shown. Determine the distance S at which a ball thrown with a velocity Vo of 100 ft/s at an angle θ = tan-1 (3/4) will strike the incline shown. θ 1 3

Example 11: In the figure, a ball thrown down the incline strikes it at a distance S = 75 m. If the ball rises to a maximum height h = 20 m. above the point of release, compute the initial velocity and the inclination θ. 20 m θ 3 S 1

Example 12: Boat A moves with a constant velocity of 6 m/sec., starting from the position down. Find θ in order for the projectile to hit the boat 5 sec. after starting, under the conditions given. How high is the hill above the water? V = 30 m/s θ 6 m/s 90 m

Example 7: A criminal is escaping across a rooftop and runs off the roof horizontally, landing on the roof of an adjacent building. The horizontal distance between the two buildings is 340 cm, and the roof of the adjacent building is 200 cm below the jumping off point. (a) What was the minimum jumping off speed needed by the criminal? (b) How long did it take the criminal to escape from one building to the other? (c) With what speed did the criminal land on the roof of the adjacent building?

Example 8: A horizontal rifle is fired at a bull’s-eye. The initial speed of the bullet is 67,000 cm/s. The barrel is pointed directly at the center of the bull’s-eye, but the bullet strikes the target at a point 2.5 com below the center. (a) How long did it take the bullet to strike the bull’s-eye? (b) What was the horizontal distance between the end of the rifle and the bull’s-eye? (c) With what velocity did the bullet strike the bull’s-eye?

Example 9: An airplane is flying with a velocity of 240 m/s at an angle of 30ᵒ below the horizontal. A flare is then released from the plane and hits a target on the ground in 13s. (a) What was the altitude of the plane when the flare was released? (b) At what horizontal distance from the plane was the target when the flare was released? (c) With what velocity did the flare hit the target?