_______________________Fired Projectile: A projectile (object) is launched horizontally with an __________________ from a height ______ . Assume no_____________________. Horizontally initial speed vi. h air resistance vi h The time in the air before landing is called the ____________________. time of flight horizontal distance traveled = _____________ the range

-9.8 m/s2 Vertical (y) motion: viy = ____ & ay = __________ displace- ment: d = vit + ½ at2 |dy| dy = viyt + ½ayt2 =0 dy = ½(-9.8)t2 dy = -4.9t2 t velocity: vf = vi +at |vfy| vfy = viy + ayt vfy = 0 + (-9.8)t t vfy = - 9.8t dropped ball The y motion is same as for a _________________.

Ex. Ball 1 is________________. Ball 2 is fired __________________ dropped Ex. Ball 1 is________________. Ball 2 is fired __________________ horizontally 1 2 vi at the same time Both reach the ground ______________________ , regardless of 2's __________________ or ________. The y motion is ______________ of the x motion. Remember: The time it takes a ______________ fired projectile to fall is ______________ the time it takes a ______________ ball to fall from the same height. initial speed mass independent horizontally equal to dropped

With no ____________________, only the force of air resistance With no ____________________, only the force of ___________ acts on the object: gravity vi The trajectory (path) is a________________. parabola gravity Air resistance acts in the direction _____________ to its velocity. This ___________________ its range. opposite decreases air resistance vi The trajectory is _____ ___________ a parabola. no longer gravity

Since the object moves in 2 dimensions, each d, v and a must be replaced by their components: For x motion: d, v, a  _______________ For y motion: d, v, a  _______________ dx, vx, ax dy, vy, ay 2. No air resistance  only ____________ , which is _______________ , in the ____ direction. There is no _________________ force. Because of this, the only acceleration a is purely vertical: ay = ___________ ax =____________ gravity downward -y horizontal or x -9.81 m/s2 horizontal 3. The initial velocity is purely _________________: viy = ___________ (initially, no y _______________) vi = ________ ("horizontally fired") component vix

Horizontal (x) motion: ax =______ displacement: d = vit + ½ at2 dx = vixt + ½axt2 dx =0 dx = vixt dx = t velocity: vf = vi +at vfx = vfx vix + axt =0 vfx = vix t vfx = uniform The x motion is _________________.

Vertical (y) motion: ______________motion same as for a ball ____________________ Horizontal (x) motion: ____________ motion ____________ x-speed accelerated uniform constant dropped from rest dy = -4.9t2 dx = vixt vfx = vfy = vix - 9.8t ay = ax = -9.8 m/s2

Ex. A 68-kg clown is fired from horizontal cannon with an initial speed of 40. m/s from a height of 25 m. What is her time of flight? 40. m/s 25 m Equation: Given: m = 68 kg vix = 40. m/s dy = -4.9t2 viy = ay = -9.81 m/s2 -25 = -4.9t2 ax = 5.1 = t2 dy = -25 m 2.3 s = t Unknown: t

What is her range? dx = vixt  dx = (40.)(2.3)  dx = 92 m What is x-component of her velocity after 1.5 s? 40. m/s What is her acceleration after 1.5 s? -9.8 m/s2 down Recalculate the new time of flight and range if she is fired with an initial speed of ____________ 80. m/s. Time of flight: range: same dx = vixt dx = (80.)(2.3) dx = 184 m

Ex. A dart fired horizontally strikes a target a distance of 0.15 m below where it is aimed. 0.15 m blow gun Equation: What was its time of flight? viy = dy = -4.9t2 ay = -9.81 m/s2 Given: -.15 = -4.9t2 ax = dy = -.15 m 0.17 s = t Unknown: t If the target was 9.0 m away from the gun, what was its initial speed? dx = vixt  9.0 = vix (0.17) vix = 53 m/s 

horizontal motion -___________ uniform dropped ball vertical motion – ______________ a = -9.8 m/s2 combined motion -________________ parabola vi 1 s 2 s 3 s 4 s 1 s 2 s 3 s 4 s

Look at how the velocity changes: vi 1 s 2 s 3 s 4 s 1 s 2 s 3 s 4 s The x-component of v is ________________ The y-component of v __________________ Resultant velocity  magnitude (speed) ______________ ___________________to trajectory constant decreases increases tangent

Which ball has the greatest acceleration? What if it was fired with half of the original vi? vi 1 s 2 s 3 s 4 s 1 s 2 s 3 s 4 s Both fall at the same rate, which equals the rate at which a dropped ball falls. Which ball has the greatest acceleration?