Question

A ball with a mass of 2 kg falls from a height of 3 m on the ground in point B. From there the ball bounces (coefficient of restitution e = 0.8) to come to the ground a little later in point C. A 3 m B 26 o The speed (in x and y direction) of the ball just before it hits the ground in point B. U o The speed (in x and y direction) of the ball just after it bounces back.

Answer 1

Solution • given qYH) mass of the → X6) ball (m)=2kg 0 ha i 37 h=3m ۷۷-) sign convention e-0.8 Bow 25 let ( The speed ( enx and Y direction) of the ball just before it hits the ground is point B Vy= vertical component of velocity just before heating the ground at B V2 = horizontal component of neberity just before heating the ground at B. Vx=0 (no any motion of the ball along horizental) now, we equation of motion along l-auis far constant acceleration from A to B y=-3001, U=0, A- -g=-9.81 m/s² V - u² = zay. (Ve); } = Vy Výro : Vy - 2X-9x-3 2X9.81X3 = 7.67 0 Vx Vy=7.67 m/s

(ii) The speed (inx and y direction) of the ball Just after it bounces back lel, Vy's vertical component of velocity after bounce back Ve = horizontal Corte 25 B V horizontal Vi= component of Vy along the plane V₂ = component of Vy, I to the plane. Vi = Vy sin 25=7.67 Sim25° V, - 3.241 mis also, V2 = Vy co$25' = 76760625° = 6.951 ms now, but after bounce back at point B ,V, will not change, V2 will be changed to eva .: Va= evaa 0:8X6.951 = 5.560ls Vhed neva Vnet V?+ V22 √(3.24 18+ [5.5682 6.435 so misi - 25 lel Voret makes an angle o with inclined plane Lano - eV2 Vi 5.56 3-241 .:0- tan' () = 59.76°

V = Vnet Cos (6-25) Vy Vnet 56-93568( 59.76-25) 0-25 125-> Ves - 5.286 mls: 25° Vy' - Voet sin (0-25) -6.435 Sin (59.76-25) 3.67 misi V,1- 5.2860ml Vy' 3-67 ols Aus at (iii) The distance (d) between point B and point c Elx' consider motion of the projectile I to the plane BC HI »X Jgsins Vy = V2 = 5.56 mls, ay = -googesi y=o .: y = Vyt + 12 ayt? 0=(5.56+X-9.816825+)xt: :tao (not bussible) -: 5.56 - (0-816825)x+ 20 itz 1.251 seconds ge4625 g 25 (

now, Va=vi consider motion of the projectile along plane BC 3:241ms, uzd, a = g sim25', t = 1.251 seconds 2 Vat + aut? 3.241x1.251 + 5*9.81 Sion 25'x (1-251)2 d- Z 7.2980 d= 7.2980 Ausa