Question

7. Rock falls can cause major damage to roads and infrastructure. To design mitigation bridges and barriers, engineers use the coefficient of restitution to model the behavior of the rocks. Rock A falls a distance of 26 m before striking an incline with a slope of a = 40°. Knowing that the coefficient of restitution between rock A and the incline is 0.2, determine the velocity of the rock after the impact and determine the distance d for where the rock will land after impact if his 30 m. (Ans: 14.93 m/s at an angle of 26.6 deg below negative x axis; d = 25.1 m)

Answer 1

Sol:- Given dofa, cocfflatne of resellution (e): 0:2 2 = 40 W = 26m. velocity of the sock upon Salling from a hou height of the Vi= lagh . 8. 9.81 m/s2 h=26 lvi Jax9.81x26 = 22.58 mis Free body Dragoam of Ball & hall e In Since Lo Statud sind zu kimisinuo -> The velocily must be caual in tangential direction before & after Impact visinuo = vasind >) 29.58 sin 40 : Nasind vasindo The coefficient of restitution blw the rock & hill --V, COSA VICOS YO-O Scanned with CamScanner

=-) We know C :0.2 (Given) 0.2 = Va cosa 22-54 cos 40° -> va cosa = 3.459] > ☺ sware & add the eq © ¢ ® va sind + va cos2 = 14.5lut 3.459² va (sin'd+cosd) = 222.62 .. 1 va = 14.92 m/s Subskibude ® V2 value in equation © 55 de cos' literature = 76.5907 the angle Below is the same yes Bus 6. The velocity of the sock afbes the imrack is 14.92 mis at an angle of 76.59" Scanned with CamScanner