Projectile Motion AP Physics C

Range-the horizontal distance that a projectile travels

Answer the following: Which launch angle produces the greatest range? 45 degrees Which launch angle obtains the greatest maximum height? 90 degrees Which launch angle has the greatest flight time? 90 degrees Which launch angle has the same range as 80 degrees? 10 degrees

Derive the Following: Derive an expression for maximum height reach by a projectile in terms of angle and initial velocity. y=(vi 2 sin2 θ)/2g Derive an expression for the range of a projectile in terms of angle and initial velocity. R=vi2sin2θ/g

Problem 1:Javelin Thrower Example An athlete throws a javelin a distance of 80 m at the equator where g = 9.78 m/s2. Four years later the Olympics are held at the North Pole where g= 9.83 m/s2. Assuming that the thrower throws the javelin with the same initial velocity as before, how far will the javelin travel at the North Pole? R=vi 2sin2 ᶱ/g R=vi2sin2ᶱ/g 80=vi2sin2ᶱ/9.78 R=782.4/9.83 vi2sin2ᶱ=782.4 R=79.6 m

Problem 2: George Washington Example It has been said that in his youth that George Washington threw a silver dollar across a river. Assuming that the river was 75 m wide, What minimum initial speed was necessary to throw the coin across the river, and How long was the coin in flight? R=vi 2sin2 ᶱ/g 75=vi2sin2(45)/10 Vi =27 m/s b) vfy=viy +ayt -27sin45=27sin45 +(-10)t t=3.9s a) 27 m/s b) 3.9 s

Thought Question 1 The figure below shows three paths for a football kicked from the ground. Ignoring the effects of air resistance, rank the paths according to (a) time of flight, (b) initial vertical velocity component, (c) initial horizontal velocity component, and (d) initial speed, greatest first. a) 1=2=3 b) 1=2=3 c) 3>2>1 d) 3>2>1

Thought Question 2 Projectile 1 is launched off a cliff with an initial speed of 100 m/s and an angle of elevation of 45 degrees. Three seconds later, a second projectile is launched off the same cliff. The instant that the first projectile has the same height as the cliff (on its way down down), the second projectile passes infinitesimally close to the first projectile without touching it (you can assume that the two trajectories intersect at a particular time, but do not worry about a physical collision between the two objects). Sketch the paths of the two projectiles and answer the following questions qualitatively. (You can choose to answer some of the following questions before finishing the sketch.) Compare the initial y-components of the velocities of the two projectiles when they are launched. Compare the maximum heights of the two projectiles and the total time spent by each projectile in the air. Compare the x-components of the positions of the peaks of the trajectories of the two projectiles. Compare the x-components of the velocities of the two projectiles. Compare the angles of elevation (at any particular time) of the velocity vectors of the two projectiles. Compare the x- and y-components of the velocities of the two projectiles as they pass each other. Which projectile has the longer range?

Thought Question 2 Answers The initial vertical component of projectile 1 is greater The maximum height and flight time of projectile 1 is greater The x component of the peaks of the two projectiles is the same The x component of projectile 2’s velocity is greater The angle of elevation of projectile 1 is greater The y component of projectile 1’s velocity is greater but the x component of projectile 2’s velocity is greater Projectile 2 has the greater range