Projectiles… Review Session

A cannonball is launched horizontally off a cliff with a speed of 100 m/s… what is its initial vertical velocity? (A) 100 m/s (B) 0 m/s (C) Need more information.

(B) 0 m/s; the initial velocity is entirely horizontal; therefore, the vertical component is zero.

A glass-bottomed airplane with a constant horizontal velocity of 150 m/s is dropping rations to folks stranded on an island. If air resistance is negligible, what does the co-pilot see looking down as the rations fall? The rations seem to fall down and back. The rations seem to fall straight down. The rations seem to fall down and forward.

(B) The rations seem to fall straight down. Both the rations and plane have the same horizontal velocity, so the rations appear to fall straight down, relative to the plane.

A ball is thrown high and straight up into the air from a truck traveling with constant velocity. In the absence of air resistance, where does the ball land? Behind the truck In front of the truck In the same spot from which it was thrown in the truck

(C) In the same spot from which it was thrown Both the ball and the truck have the same horizontal velocity, so each second, the truck moves forward, so moves the ball.

In your hand Behind you In front of you You flip a coin straight up into the air while on an airplane that is accelerating in preparation for take off. Where does the coin land??? In your hand Behind you In front of you

(B) Behind you The coin has the same horizontal velocity of the plane when it was released. In the air, its horizontal velocity remains the same, though the plane (and you) are accelerating… therefore, it lands behind you. accelerating vf vi Horizontal velocity is constant vx

(A) 70 m/s (B) 50 m/s (C) 40 m/s (D) 30 m/s A ball is kicked into the air such that the horizontal component of its initial velocity is 30 m/s and the vertical component is 40 m/s. What is the initial speed of the ball? (A) 70 m/s (B) 50 m/s (C) 40 m/s (D) 30 m/s 30 m/s 40 m/s

(B) 50 m/s Speed is the magnitude of velocity. The velocity is the vector sum of the horizontal and vertical components: (40 m/s)2 + (30 m/s)2 = (50 m/s)2 30 m/s 40 m/s

A ball is kicked into the air such that the horizontal component of its initial velocity is 30 m/s and the vertical component is 40 m/s. What is the speed of the ball just before it strikes the ground? (A) 70 m/s (B) 50 m/s (C) 40 m/s (D) 30 m/s (E) 0 m/s 30 m/s 40 m/s

(B) 50 m/s The horizontal velocity remains 30 m/s and the vertical component is -40 m/s just before the ball strikes. Vy (m/s) t (s) Vertical Velocity vs. Time 40 -40 30 m/s 40 m/s

Three soccer balls are kicked from the ground Three soccer balls are kicked from the ground. Their trajectories are shown. Which ball has the greatest vertical component of its initial velocity? (A) (B) (C) (D) They’re all the same.

(D) They’re all the same. Analyzing the motions from launches to the heights of trajectories: yA = yB = yC vAf = vBf = vCf = 0 aA = aB = aC = 9.8 m/s2 Using the equation vf2 = vi2 + 2a y will yield the same value for vi for each kick. (A) (B) (C)

Three soccer balls are kicked from the ground Three soccer balls are kicked from the ground. Their trajectories are shown. Which ball is in air longer? (A) (B) (C) (D) They’re all in the air the same amount of time

(D) They’re all in the air the same amount of time. Analyzing the motions from highest point to striking the ground: yA = yB = yC vAi = vBi = vCi = 0 aA = aB = aC = 9.8 m/s2 Using the equation y = vit + ½ at2 will yield the same value for each kick. (A) (B) (C)

Three soccer balls are kicked from the ground Three soccer balls are kicked from the ground. Their trajectories are shown. Which ball has the greatest speed throughout its trajectory? (A) (B) (C) (D) They all have the same speed throughout.

(C) Since the balls are in the air for the same amount of time, C must have the greatest horizontal velocity because it has the greatest horizontal displacement: x = vxt (A) (B) (C)

(C)Cannot be determined. A soccer ball is kicked up into the air and passes two identical windows, A and B, as shown. The ball takes more time passing which window (vertically)? (A) A (B) B (C)Cannot be determined. (B) (A)

(B) The ball takes more time passing window B because the speed of the ball is decreasing as it rises. If its average speed is less as it crosses window B, the time it will take to pass will be greater. (B) (A)

(D) They all strike with the same speed. Three projectiles are launched as shown, each with the same initial velocity of 25 m/s at an angle of 65 degrees. Rank the situations according to the speed with which they strike the ground, greatest first. (A) 1 2 3 (B) 2 3 1 (C) 3 2 1 (D) They all strike with the same speed. 65 (1) (2) (3)

(C) 3 2 1 The projectiles speed decreases to its minimum value at the top of its trajectory, then speeds up on the way down. Hits with same speed as launch speed Hits with less speed than launch speed Hits with more speed than launch speed 65 (1) (2) (3)

(C) They both hit at the same time A bullet is fired horizontally from a gun. At the same time the bullet exits the barrel, a second bullet is dropped from the same height as the gun barrel. Which bullet strikes the ground first (neglect air resistance and curvature of the earth). (A) The fired bullet (B) The dropped bullet (C) They both hit at the same time

(C) They both hit at the same time Analyzing the motions from highest point to striking the ground: ybullet fired = ybullet dropped vi bullet fired = vi bullet fired = 0 acceleration for both = 9.8 m/s2 Vertical data is the same, so the time that they hit the ground will be the same as well.