Lecture 4 Ch 4 TWO AND THREEDIMENSIONAL MOTION

Lecture 4 Ch 4. TWO- AND THREE-DIMENSIONAL MOTION University Physics: Mechanics Iksan Bukhori, M. Phil iksan. bukhori@president. ac. id Original Presentation by Dr. –Ing Erwin Sitompul 2018

Projectile Motion § Projectile motion: a motion in a vertical plane, where the → acceleration is always the free-fall acceleration g, which is downward. § Many sports involve the projectile motion of a ball. § Besides sports, many acts also involve the projectile motion. Iksan Bukhori University Physics: Mechanics 1/2

Projectile Motion § Projectile motion consists of horizontal motion and vertical motion, which are independent to each other. § The horizontal motion has no acceleration (it has a constant velocity). § The vertical motion is a free fall motion with constant acceleration due to gravitational force. Iksan Bukhori University Physics: Mechanics 1/3

Projectile Motion Iksan Bukhori University Physics: Mechanics 1/4

Projectile Motion Two Golf Balls • The vertical motions are quasiidentical. • The horizontal motions are different. Iksan Bukhori University Physics: Mechanics 1/5

Projectile Motion Analyzed The Horizontal Motion The Vertical Motion Iksan Bukhori University Physics: Mechanics 1/6

Projectile Motion Analyzed The Horizontal Range vx = v 0 x vy = –v 0 y Eliminating t, • This equation is valid if the landing height is identical with the launch height. Iksan Bukhori University Physics: Mechanics 1/7

Projectile Motion Analyzed Further examining the equation, Using the identity we obtain R is maximum when sin 2θ 0 = 1 or θ 0 =45°. Iksan Bukhori • If the launch height and the landing height are the same, then the maximum horizontal range is achieved if the launch angle is 45°. University Physics: Mechanics 1/8

Symmetry of Position and Speed v 0 y = 29. 4 m/s • If the initial elevation and final elevation are the same, the velocity of an object at each elevation will be the same in magnitude , but opposite in direction. • The object’s height and the speed will be symmetrical around the time when the peak position is reached. Iksan Bukhori University Physics: Mechanics 1/9

Projectile Motion Analyzed • The launch height and the landing height differ. • The launch angle 45° does not yield the maximum horizontal distance. Iksan Bukhori University Physics: Mechanics 1/10

Projectile Motion Analyzed The Effects of the Air § Path I: Projectile movement if the air resistance is taken into account § Path II: Projectile movement if the air resistance is neglected (as in a vacuum) Our calculation along this chapter is based on this assumption Iksan Bukhori University Physics: Mechanics 1/11

Example: Baseball Pitcher A pitcher throws a baseball at speed 40 km/h and at angle θ = 30°. h (a) Determine the maximum height h of the baseball above the ground. Iksan Bukhori University Physics: Mechanics 1/12

Example: Baseball Pitcher A pitcher throws a baseball at speed 40 km/h and at angle θ = 30°. d (b) Determine the duration when the baseball is on the air. (c) Determine the horizontal distance d it travels. Iksan Bukhori University Physics: Mechanics 1/13

Simulation: How to Fire the Cannon? v 0 9 m θ 16 m A cannon is 1. 20 m above the ground. You may adjust the initial speed and the angle of fire of the cannon. If the target is horizontally 16 m away from the cannon and at 9 m above the ground, how do you set the cannon so that the projectile can hit the target? Iksan Bukhori 00 University Physics: Mechanics 1/14

Example: Rescue Plane A rescue plane flies at 198 km/h and constant height h = 500 m toward a point directly over a victim, where a rescue capsule is to land. (a) What should be the angle Φ of the pilot’s line of sight to the victim when the capsule release is made? Iksan Bukhori Released horizontally University Physics: Mechanics 1/15

Example: Rescue Plane A rescue plane flies at 198 km/h and constant height h = 500 m toward a point directly over a victim, where a rescue capsule is to land. (b) As the capsule reaches the → water, what is its velocity v in unit-vector notation and in magnitude-angle notation? Released horizontally Unit-vector notation Magnitude-angle notation Iksan Bukhori University Physics: Mechanics 1/16

Example: Clever Stuntman A stuntman plans a spectacular jump from a higher building to a lower one, as can be observed in the next figure. Can he make the jump and safely reach the lower building? Time for the stuntman to fall 4. 8 m He cannot make the jump Horizontal distance jumped by the stuntman in 0. 99 s Iksan Bukhori University Physics: Mechanics 1/17

A stone is thrown from the top of a building upward at an angle of 30. 0° to the horizontal and with an initial speed of 20. 0 m/s. If the height of the building is 45. 0 m, (a) how long is it before the stone hits the ground? (b) What is the speed of the stone just before it strikes the ground? (c) Where does the stone strike the ground as measured from the base of the building? Iksan Bukhori University Physics: Mechanics 1/18

Homework 5 1. A basketball player who is 2. 00 m tall is standing on the floor 10. 0 m from the basket. If he shoots the ball at a 40. 0° angle with the horizontal, at what initial speed must he throw so that it goes through the hoop without striking the backboard? The basket height is 3. 05 m. Iksan Bukhori University Physics: Mechanics 1/19

Homework 5 2. A dart player throws a dart horizontally at 12. 4 m/s. The dart hits the board 0. 32 m below the height from which it was thrown. How far away is the player from the board? 3. As a ship is approaching the dock at 45. 0 cm/s, an important piece of landing equipment needs to be thrown to it before it can dock. This equipment is thrown at 15. 0 m/s at 60. 0° above the horizontal from the top of a tower at the edge of the water, 8. 75 m above the ship’s deck. For this equipment to land at the front of the ship, at what distance D from the dock should the ship be when the equipment is thrown? Air resistance can be neglected. Iksan Bukhori University Physics: Mechanics 1/20