Relative Velocity. Exercise

Transcription

1 PHYSICS 0 Lecture 06 Projectile Motion Tetbook Sections 4. Lecture 6 Purdue Universit, Phsics 0 1 Relative Velocit We often assume that our reference frame is attached to the Earth. What happen when the reference frame is moving at a constant velocit with respect to the Earth? The motion can be eplained b including the relative velocit of the reference frame in the description of the motion. The ground velocit of an airplane is the vector sum of the air velocit and the wind velocit. Using the air as the intermediate reference frame, ground speed is: Eample airplane V(PG)=V(PA) +V(AG) Lecture 6 Purdue Universit, Phsics 0 Eercise Three swimmers can swim equall fast relative to the water. The have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carl (C) swims downstream. Which swimmer wins the race? Eercise What angle should Ann take to get directl to the other side if she can swim 5 mph relative to the water, and the river is flowing at 3 mph? A) Ann B) Beth C) Carl correct V Ann,ground = V ann,water +V water,ground t = d / v Ann v = v cos() Beth v = v Carl v = v cos() A B C Lecture 6 Purdue Universit, Phsics 0 3 -direction: sin() = V water,ground / V ann,water A B C sin() = 3/5 Lecture 6 Purdue Universit, Phsics 0 4

2 X and Y are -Dimensions INDEPENDENT No component of one F or v on other The don t have to be vertical and horizontal just at right angles to each other Break -D problem into two 1-D problems Demo 1D-1 was done in L04 Velocit in Two Dimensions A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 5 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s. What is the magnitude of the change in velocit? -direction v i = 5 m/s v f = 3 m/s cos(5) "v = 3cos(5) 5 =-.8m/s v = v + v =.6 m/s 5 m/s -direction v i = 0 m/s v f = 3 m/s sin(5) "v = 3sin(5)=+1.7 m/s 3 m/s Lecture 6 Purdue Universit, Phsics 0 5 Lecture 6 Purdue Universit, Phsics 0 6 Acceleration in Two Dimensions A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 5 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s. What is the average acceleration? -direction a =.8m/s 0.5 s -direction = 4.56 m/s a = 1.7m/s 0.5 s =.54 m/s Kinematics in Two Dimensions = 0 + v 0 t + 1/ a t = 0 + v 0 t + 1/ a t v = v 0 + a t v = v 0 + a t v = v 0 + a " v = v 0 + a " a = a + a 5 m/s = 5.1 m/s 3 m/s and motions are independent The share a common time t Lecture 6 Purdue Universit, Phsics 0 7 Lecture 6 Purdue Universit, Phsics 0 8

3 Projectile Motion Velocit of a Projectile -direction: a = 0 -direction: a = -g = 0 + v 0 t v = v 0 = 0 + v 0 t - gt v = v 0 g t v = v 0 g " Velocit components of a projectile Lecture 6 Purdue Universit, Phsics 0 9 Lecture 6 Purdue Universit, Phsics 0 10 Independence of the Vertical and Horizontal motion of Projectiles A place-kicker kicks a football at an angle of =40 0 above the horizontal ais. The initial speed of the ball is v 0 = m/s. Ignore air resistance and find the range R that the ball attains. v 0 =m/s =40 0 H R Lecture 6 Purdue Universit, Phsics 0 11 Lecture 6 Purdue Universit, Phsics 0 1

4 Use the equations = 0 + v 0 t v = v 0 v 0 = v 0 cos = (m/s)cos 40 0 = 17 m/s = 0 + v 0 t - 1/ gt v = v 0 - gt v = v 0 - g " The range is a characteristic of the horizontal motion You need v 0 and v 0 but ou have been given v 0 v 0 v 0 v 0 Lecture 6 Purdue Universit, Phsics 0 13 We could be done if we know the time of flight of the kickoff = R = v 0 t The time of flight can be determined from equations. For eample the time to get to height H is v 0 v 0 v = v 0 gt v 0 t h = v v 0 = 14m / s v 0 =v 0 sin = g 9.8m / s = 1.48s (m/s)sin 40 0 =14 m/s Therefore the time to determine the range is #.9 s = R = v 0 t = (17m / s)(.9s) = 49m The range depends on the angle at which the football is kicked. Maimum range is reached for =45 0 Lecture 6 Purdue Universit, Phsics 0 14 Range of a Projectile Demo 1D- Two was to hit a target ecept at limit Lecture 6 Purdue Universit, Phsics 0 15

5 Shooting the Monke You are a vet tring to shoot a tranquilizer dart into a monke hanging from a branch in a distant tree. You know that the monke is ver nervous, and will let go of the branch and start to fall as soon as our gun goes off. On the other hand, ou also know that the dart will not travel in a straight line, but rather in a parabolic path like an other projectile. In order to hit the monke with the dart, where should ou point the gun before shooting? A) Right at the monke B) Below the monke C) Above the monke Demo 1D-3 = v 0 t - 1 / g t Shooting the Monke = 0-1 / g t Dart hits the monke Lecture 6 Purdue Universit, Phsics 0 17 Lecture 6 Purdue Universit, Phsics 0 18