Motion in Two Dimensions Projectile Motion A projectile

Motion in Two Dimensions

Projectile Motion A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola.

Motion in Two Dimensions

Motion in Two Dimensions ax = 0 ay = -g

Motion in Two Dimensions Ignoring air resistance, the horizontal component of a projectile's acceleration (A) is zero. (B) remains a non-zero constant. (C) continuously increases. (D) continuously decreases.

Motion in Two Dimensions If an object is launched at an initial angle of θ 0 with the horizontal, the analysis is similar except that the initial velocity has a vertical component. q

Motion in Two Dimensions Ignoring air resistance, the horizontal component of a projectile's velocity (A) is zero. (B) remains constant. (C) continuously increases. (D) continuously decreases.

Motion in Two Dimensions y Constant acceleration vo q x Constant velocity Eq 1 Eq 2

Motion in Two Dimensions A ball is thrown with a velocity of 20 m/s at an angle of 60° above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory? (A) 10 m/s (B) 17 m/s (C) 20 m/s (D) zero

Motion in Two Dimensions y Constant velocity vo q x Sub Eq 1 Eq 3

Practice Problem Vx If Vx = 6. 80 units and Vy = -7. 40 units, a) determine the magnitude of V. q Vy V b) determine the direction of V

Motion in Two Dimensions y Constant acceleration vo q x Eq 4

Motion in Two Dimensions A soccer ball is kicked with a velocity of 25 m/s at an angle of 45° above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory? (A) 9. 80 m/s 2 downward (B) (9. 80 m/s 2) × sin (45°) downward (C) (9. 80 m/s 2) × sin (45°) upward (D) (9. 80 m/s 2) upward

Motion in Two Dimensions When a football in a field goal attempt reaches its maximum height, how does its speed compare to its initial speed? (A) It is zero. (B) It is equal to its initial speed. (C) It is greater than its initial speed. (D) It is less than its initial speed.

Motion in Two Dimensions Vertical Position as a Function of Horizontal Displacement y vo q h x Solve Eq 3 for t Sub into Eq 4 Eq 5

Motion in Two Dimensions Maximum Height y vo q h x Sub into Eq 4 At the maximum height (vy = 0) Eq 6 Eq 7

Problem A football is kicked at ground level with a speed of 18. 0 m/s at an angle of 35. 0º to the horizontal. How much later does it hit the ground? Time in the air is twice the time to the top.

Motion in Two Dimensions y Range vo q h x R Eq 8

Motion in Two Dimensions At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range? (A) 0° (B) 30° (C) 45° (D) 60°

Motion in Two Dimensions The range of a projectile is maximum (if there is no air resistance) for a launch angle of 45°.

Problem A projectile is fired with an initial speed of 65. 2 m/s at an angle of 34. 5º above the horizontal on a long flat firing range. Determine (a) the maximum height reached by the projectile. (b) the total time in the air (c) the total horizontal distance covered (that is, the range).

Question 3. 10 a Shoot the Monkey I You are trying to hit a friend with a water balloon. He is sitting in the window of his dorm room directly across the street. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him? Your friend falls under the influence of gravity, just like the water balloon. Thus, they are both undergoing free fall in the ydirection. Since the slingshot was accurately aimed at the right height, the water balloon will fall exactly as your friend does, and it will hit him!! a) yes, it hits b) maybe—it depends on the speed of the shot c) no, it misses d) the shot is impossible e) not really sure Assume that the shot does have enough speed to reach the dorm across the street.

Shoot the Monkey

Equations Horizontal Velocity Eq 1 Vertical Velocity Eq 2 Horizontal Displacement Eq 3 Vertical Displacement Eq 4

Equations Vertical Position Eq 5 Time to the Top Eq 6 Maximum Height Eq 7 Range Eq 8