‫ﺟﺎﻣﻌﺔ ﺍﳌﻠﻚ ﺳﻌﻮﺩ‬ ‫ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ‬ ‫ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎء ﻭﺍﻟﻔﻠﻚ‬ ‫(‬ ‫ﲤﺎﺭﻳﻦ ﺍﻟﻔﺼﻞ ﺍﻟﺮﺍﺑﻊ ﳌﻘﺮﺭ ‪ ١٠٣‬ﻓﻴﺰ ) ﺍﻟﻔﺼﻞ ﺍﻟﺪﺭﺍﺳﻲ‬ ‫ﺩ‪ ٠‬ﻋﺒﺪﺍﷲ ﳏﻤﺪ ﺍﻟﺰﻳـﺮ‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻷﻭﻝ‪:‬‬ ‫‪y‬‬ ‫ﺍﺤﺴﺏ ﻤﻘﺩﺍﺭ ﻭﺍﺘﺠﺎﻩ ﻤﺤﺼﻠﺔ ﺍﻟﻘﻭﻱ ﺍﻟﻤﺒﻴﻨﺔ ﻓﻰ ﺍﻟﺸﻜل‪:‬‬ ‫‪40 N‬‬ ‫‪63‬‬ ‫‪30 N‬‬ ‫‪x‬‬ ‫‪120‬‬ ‫‪310‬‬ ‫‪ANS: |R|=39.4 N, θ=49.5°‬‬ ‫‪15 N‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﺜﺎﻧﻲ‪:‬‬ ‫ﻴﺸﺎﻫﺩ ﻁﻔل ﺠﺴﻡ ﻴﺼﻌﺩ ﺇﻟﻰ ﺃﻋﻠﻰ ﻭﻴﻌﻭﺩ ﺇﻟﻰ ﺃﺴﻔل ﻋﺒﺭ ﻨﺎﻓﺫﺓ ﺍﺭﺘﻔﺎﻋﻬﺎ )ﻋﺭﺽ ﻓﺘﺤﺘﻬﺎ( ‪ ، 1.5 m‬ﺇﺫﺍ ﻜﺎﻥ‬ ‫ﺍﻟﺯﻤﻥ ﺍﻟﻜﻠﻲ ﻟﻠﺠﺴﻡ ﻟﻜﻲ ﻴﻜﻭﻥ ﻓﻲ ﻤﺠﺎل ﺭﺅﻴﺔ ﺍﻟﻁﻔل ﻴﺴﺎﻭﻱ ‪ 1 sec‬ﻓﺎﺤﺴﺏ ﺍﻻﺭﺘﻔﺎﻉ ﺍﻟﺫﻱ ﻴـﺼﻌﺩ ﺇﻟﻴـﻪ‬ ‫?‬ ‫ﺍﻟﺠﺴﻡ ﺃﻋﻠﻰ ﺍﻟﻨﺎﻓﺫﺓ‪٠‬‬ ‫‪1.5 m‬‬ ‫‪ANS: ?=1.54 cm‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﺜﺎﻟﺚ‪:‬‬ ‫ﻴﻘﻔﺯ ﻤﻅﻠﻲ ﻤﻥ ﺍﺭﺘﻔﺎﻉ ﻤﺎ ﺒﺩﻭﻥ ﺍﺤﺘﻜﺎﻙ )ﻤﻘﺎﻭﻤﺔ ﻫﻭﺍﺀ(‪ ٠‬ﻭﺒﻌﺩ ﺴﻘﻭﻁﻪ ﻤﺴﺎﻓﺔ ‪ 50 m‬ﻓﺘﺢ ﻤﻅﻠﺘﻪ ﻭﺘﺒﺎﻁﺄ ﺒﻤﻘﺩﺍﺭ ‪ 2 m/s‬ﺤﺘﻰ ﻭﺼل‬ ‫‪2‬‬ ‫ﺇﻟﻰ ﺍﻷﺭﺽ ﺒﺴﺭﻋﺔ ‪ ، 3 m/s‬ﺍﺤﺴﺏ‪) :‬ﺃ( ﺍﻟﺯﻤﻥ ﺍﻟﺫﻱ ﻴﺴﺘﻐﺭﻗﻪ ﺍﻟﻤﻅﻠﻲ ﻓﻲ ﺍﻟﻬﻭﺍﺀ‪) ٠‬ﺏ( ﺍﻻﺭﺘﻔﺎﻉ ﺍﻟﺫﻱ ﻴﺴﻘﻁ ﻤﻨﻪ ﺍﻟﻤﻅﻠﻲ‪٠‬‬ ‫‪Ans: (a) 17.4 s (b) 293 m‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﺮﺍﺑﻊ‪:‬‬ ‫ﻴﺴﻘﻁ ﺠﺴﻡ ﻤﻥ ﻁﺎﺌﺭﺓ ﺘﺤﻠﻕ ﻋﻠﻰ ﺍﺭﺘﻔﺎﻉ ‪ 1500 m‬ﻭﺴﺭﻋﺘﻬﺎ ﺘﺴـــﺎﻭﻱ ‪500 km/h‬‬ ‫)ﺍ( ﺍﺤﺴﺏ ﺍﻟﺯﻤﻥ ﺍﻟﺫﻱ ﻴﺴﺘﻐﺭﻗﻪ ﺍﻟﺠﺴﻡ ﻟﻠﻭﺼﻭل ﺍﻟﻰ ﺍﻷﺭﺽ ‪٠‬‬ ‫)ﺏ( ﺍﺤﺴﺏ ﺍﻟﻤﺴﺎﻓﺔ ﺍﻷﻓﻘﻴﺔ ﻤﻨﺫ ﻟﺤﻅﺔ ﺴﻘﻭﻁ ﺍﻟﺠﺴﻡ ﺤﺘﻰ ﺍﻻﺼﻁﺩﺍﻡ ﺒﺎﻷﺭﺽ‪٠‬‬ ‫)ﺠـ( ﺍﺤﺴﺏ ﺴﺭﻋﺔ ﺍﺼﻁﺩﺍﻡ ﺍﻟﺠﺴﻡ ﺒﺎﻷﺭﺽ‪٠‬‬ ‫‪ANS: (a) 17.5 s (b) 2431 m (c) |v|=220.5 m/s, θ=-50°‬‬ ‫‪Page 1 of 6‬‬ ‫‪Dr. Abdallah M. Azzeer‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﳋﺎﻣﺲ‪:‬‬ ‫ﺃﻁﻠﻘﺕ ﺭﺼﺎﺼﺔ ﺃﻓﻘﻴﺎ ﻋﻠﻰ ﻫﺩﻑ ﻴﺒﻌﺩ ﻤﺴﺎﻓﺔ ‪ 100 m‬ﻓﺈﺫﺍ ﻜﺎﻥ ﺍﻟﺯﻤﻥ ﺍﻟﺫﻱ ﺍﺴﺘﻐﺭﻗﺘﻪ ﺍﻟﺭﺼﺎﺼﺔ ﺤﺘـﻰ ﺘـﺼﻁﺩﻡ ﺒﺎﻟﻬـﺩﻑ ﻴـﺴـﺎﻭﻱ‬ ‫‪ 0.075 s‬ﻓﺎﺤﺴﺏ ‪ (١):‬ﺍﻟﻤﺴﺎﻓﺔ ﺍﻟﻌﻤﻭﺩﻴﺔ ﻋﻠﻰ ﺍﻟﻬﺩﻑ ﻨﺘﻴﺠﺔ ﺍﻨﺤﺭﺍﻑ ﺍﻟﺭﺼﺎﺼﺔ ﻋﻥ ﻤﺴﺎﺭﻫﺎ ﺍﻷﻓﻘﻲ ﺒـﺴﺒﺏ ﻭﺯﻨﻬـﺎ ‪ (٢) ٠‬ﺴـﺭﻋﺔ‬ ‫ﺍﺼﻁﺩﺍﻡ ﺍﻟﺭﺼﺎﺼﺔ ﺒﺎﻟﻬﺩﻑ ‪٠‬‬ ‫‪ANS: (1) 2.76 cm (2) |v|= 1333.3 m/s , θ=-0.03°‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﺴﺎﺩﺱ‪:‬‬ ‫ﺘﺘﺩﺤﺭﺝ ﻜﺭﺓ ﻤﻥ ﺃﻋﻠﻰ ﺤﺎﻓﺔ ﻁﺎﻭﻟﺔ ﺍﺭﺘﻔﺎﻋﻬﺎ ‪ 1 m‬ﻤﻥ ﺴﻁﺢ ﺍﻷﺭﺽ ﺒﺴﺭﻋﺔ ﻤﻘﺩﺍﺭﻫﺎ ‪ 1 m/s‬ﺍﺤﺴﺏ ‪) :‬ﺃ( ﺍﻟﺯﻤﻥ ﺍﻟﺫﻱ ﺘﺴﺘﻐﺭﻗﻪ ﺍﻟﻜﺭﺓ‬ ‫ﻗﺒل ﺴﻘﻭﻁﻬﺎ ﻋﻠﻰ ﺍﻷﺭﺽ ‪) .‬ﺏ( ﺍﻟﻤﺴﺎﻓﺔ ﺍﻷﻓﻘﻴﺔ ﻟﻤﻜﺎﻥ ﺴﻘﻭﻁ ﺍﻟﻜﺭﺓ ﻋﻠﻰ ﺍﻷﺭﺽ ‪) .‬ﺩ( ﺴﺭﻋﺔ ﺍﻟﻜﺭﺓ )ﻤﻘﺩﺍﺭﺍ ﻭﺍﺘﺠﺎﻫﺎ(‬ ‫‪ANS: (a) 0.45 s (b) 0.45 m (c) |v|=4.52 m/s , θ=-77.2°‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﺴﺎﺑﻊ‪:‬‬ ‫ﺃﻁﻠﻘﺕ ﻗﺫﻴﻔﺔ ﺒﺯﺍﻭﻴﺔ ‪ 45°‬ﻤﻊ ﺍﻷﻓﻘﻰ ﺒﺴﺭﻋﺔ ﺍﺒﺘﺩﺍﺌﻴﺔ ‪ vo‬ﻜﻤﺎ ﻫﻭ ﻤﺒﻴﻥ ﻓﻲ ﺍﻟﺸﻜل‪ ٠‬ﺍﺤﺴﺏ‪:‬‬ ‫‪y‬‬ ‫‪v0‬‬ ‫)ﺃ( ﺍﻟﺯﻤﻥ ﺍﻟﺫﻱ ﺘﺴﺘﻐﺭﻗﻪ ﺍﻟﻤﻘﺫﻭﻓﺔ ﻟﺘﺼل ﺇﻟﻲ ﺍﻟﻨﻘﻁﺔ ﺫﺍﺕ ﺍﻹﺤﺩﺍﺜﻴﺎﺕ ‪ x = 86.6 m‬ﻭ ‪.y = 50 m‬‬ ‫)ﺏ( ﺴﺭﻋﺘﻬﺎ ﺍﻻﺒﺘﺩﺍﺌﻴﺔ ‪.vo‬‬ ‫‪(86.6,50) m‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﺜﺎﻣﻦ‪:‬‬ ‫‪45o‬‬ ‫‪x‬‬ ‫‪y‬‬ ‫ﻭﺠﻪ ﻤﺩﻓﻊ ﺇﻟﻰ ﻫﺩﻑ ﻜﻤﺎ ﻫﻭ ﻤﺒﻴﻥ ﻓﻲ ﺍﻟﺸﻜل‪ .‬ﺃﺴﺘﺨﺩﻡ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﺍﻟﻭﺍﺭﺩﺓ ﻟﺤﺴﺎﺏ‪:‬‬ ‫)ﺃ( ﺍﻟﻭﻗﺕ ﺍﻟﺫﻱ ﺘﺴﺘﻐﺭﻗﻪ ﺍﻟﻘﺫﻴﻔﺔ ﻟﻠﻭﺼﻭل ﺇﻟﻰ ﺍﻟﻬﺩﻑ‪.‬‬ ‫)ﺏ( ﻤﻭﻗﻊ ﺍﻟﻘﺫﻴﻔﺔ ﻋﻠﻰ ﺍﻟﻤﺤﻭﺭ )‪ (y‬ﺍﻟﻌﻤﻭﺩﻱ‪.‬‬ ‫)ﺝ( ﺍﻟﺴﺭﻋﺔ ﺍﻻﺒﺘﺩﺍﺌﻴﺔ ﻟﻠﻘﺫﻴﻔﺔ ﻜﻲ ﺘﺼﻴﺏ ﺍﻟﻬﺩﻑ ﻋﻨﺩ ﺍﻟﻨﻘﻁﺔ‪. O‬‬ ‫‪300 m‬‬ ‫‪O‬‬ ‫‪200 m/s‬‬ ‫‪100‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﺘﺎﺳﻊ‪:‬‬ ‫ﻗﺫﻓﺕ ﻜﺭﺓ ﺒﺴﺭﻋﺔ ﺍﺒﺘﺩﺍﺌﻴﺔ ﻤﻘﺩﺍﺭﻫﺎ ‪ 6 m/s‬ﻭﺒﺯﺍﻭﻴﺔ ‪ 40°‬ﺃﻋﻠﻲ ﺍﻷﻓﻕ ﻤﻥ ﺴﻁﺢ ﻤﺒﻨـﻲ‬ ‫ﺒﺎﺘﺠﺎﻩ ﻤﺒﻨﻲ ﻤﺭﺘﻔﻊ ﺁﺨﺭ ﻴﺒﻌﺩ ‪ ، 15 m‬ﺍﺤﺴﺏ ﺍﻟﻤﺴﺎﻓﺔ ﺍﻟﺭﺃﺴﻴﺔ ﺍﻋﻠﻲ ﺃﻭ ﺍﺴﻔل ﻤـﺴﺘﻭﻱ‬ ‫ﺍﻟﻘﺫﻑ ﻟﻤﻜﺎﻥ ﺍﺼﻁﺩﺍﻡ ﺍﻟﻜﺭﺓ ﺒﺎﻟﻤﺒﻨﻲ ﺍﻟﻤﺭﺘﻔﻊ‪٠‬‬ ‫‪40‬‬ ‫‪15 m‬‬ ‫‪ANS: 39.4 m below its original level‬‬ ‫‪Page 2 of 6‬‬ ‫‪Dr. Abdallah M. Azzeer‬‬ ‫ﺍﻟﺴﺆﺍﻝ ﺍﻟﻌﺎﺷﺮ‪:‬‬ ‫ﻴﺭﻏﺏ ﺴﺎﺌﻕ ﺩﺭﺍﺠﺔ ﻨﺎﺭﻴﺔ ﺍﻟﻘﻔﺯ ﻋﺒﺭ ﻨﻬﺭ ﻋﺭﻀﻪ ‪ ، 25 m‬ﺇﺫﺍ ﻜﺎﻨﺕ ﺯﺍﻭﻴﺔ ﻤﻴل ﺤﺎﺠﺯ ﺍﻟﻘﻔﺯ ﺘﺴﺎﻭﻱ ‪ 37°‬ﻭﻤﺴﺘﻭﻱ ﺍﻟﻨﻬﺭ ﻤﻥ ﺍﻟﺠﺎﻨـﺏ‬ ‫ﺍﻵﺨﺭ ﻤﺴﺎﻭﻴ ﹰﺎ ﻟﻤﺴﺘﻭﺍﻩ ﻓﻲ ﺍﻟﺠﺎﻨﺏ ﺍﻷﻭل ﻜﻤﺎ ﻫﻭ ﻤﺒﻴﻥ ﻓﻲ ﺍﻟﺸﻜل ﻓﺄﺤﺴﺏ‪:‬‬ ‫)ﺃ( ﺴﺭﻋﺔ ﺍﻟﺴﺎﺌﻕ ﻋﻨﺩ ﻗﻤﺔ ﺍﻟﺤﺎﺠﺯ ﺤﺘﻰ ﻴﺘﺠﺎﻭﺯ ﺍﻟﻨﻬﺭ ﻭﻴﻨﺯل ﺍﻟﻲ ﺍﻟﺠﺎﻨﺏ ﺍﻵﺨـﺭ‬ ‫ﺒﺄﻤﺎﻥ‪٠‬‬ ‫‪37‬‬ ‫)ﺏ( ﺍﻟﺯﻤﻥ ﺍﻟﻜﻠﻲ ﺍﻟﺫﻱ ﻴﺴﺘﻐﺭﻗﻪ ﺍﻟﺴﺎﺌﻕ ﻟﺘﺠﺎﻭﺯ ﺍﻟﻨﻬﺭ‪٠‬‬ ‫‪25 m‬‬ ‫‪ANS: (a) 15.96 m/s (b) 1.96 s‬‬ ‫‪Page 3 of 6‬‬ ‫‪Dr. Abdallah M. Azzeer‬‬ KING SAUD UNIVERSITY PHYSICS & ASTRONOMY DEPARTMENT 103-Phys (Dr.ABDALLAH M. AZZEER) WRITE YOUR ANSWER ON THE ATTACHED SHEET r 1. If a = 28 ˆi + 11 ˆj and b is as shown, what is the magnitude of the sum of these two y vectors? a. 45 b b. 35 40° c. 39 25 x d. 32 e. 64 2. The three forces shown act on a particle. What is the magnitude of the resultant of these three forces? y a. 27 N 65 N b. 33 N 30° x 30 N c. 36 N d. 24 N 20° e. 105 N 20 N 3. An object is released from rest at an unknown height h above the ground. One second later a second object is released from rest at the same height. When the first object strikes the ground, the second is 20 m above the ground. What is the initial height h? a. 32 m b. 45 m c. 40 m d. 36 m e. 54 m r r 4. If A = 12 ˆi - 16 ˆj and B = - 24 ˆi + 10 ˆj , what is the magnitude of the vector r r r C = 2A − B ? a. 42 b. 22 c. 64 d. 90 e. 13 5. If A = 12i - 16j and B = -24i + 10j, what is the direction of the vector C = 2A - B? a. -49 b. -41 c. -90 d. +49 e. 221 6. A projectile is thrown from the top of a building with an initial velocity of 30 m/s in the horizontal direction. If the top of the building is 30 m above the ground, how fast will the projectile be moving just before it strikes the ground? a. 35 m/s b. 39 m/s c. 31 m/s d. 43 m/s e. 54 m/s 7. A stone is thrown from the top of a building with an initial velocity of 20 m/s downward. The top of the building is 60 m above the ground. How much time elapses between the instant of release and the instant of impact with the ground? a. 2.0 s Dr. Abdallah M. Azzeer b. 6.1 s c. 3.5 s d. 1.6 s e. 1.0 s Page 4 of 6 8. The initial speed of a cannon ball is 200 m/s. If the ball is to strike a target that is at a horizontal distance of 3.0 km from the cannon, what is the minimum time of flight for the ball? a. 16 s b. 21 s c. 24 s d. 14 s e. 19 s 9. A ball thrown vertically from ground level is caught 3.0 s later by a person on a balcony which is 14 m above the ground. Determine the initial speed of the ball. a. 19 m/s b. 4.7 m/s c. 10 m/s d. 34 m/s e. 17 m/s 10. A racecar moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the racecar? a. 8.8 m/s2 b. 7.5 m/s2 c. 9.4 m/s2 d. 6.3 m/s2 e. 5.3 m/s2 Dr. Abdallah M. Azzeer Page 5 of 6 KING SAUD UNIVERSITY PHYSICS & ASTRONOMY DEPARTMENT 103-Phys (Dr.ABDALLAH M. AZZEER) WRITE YOUR ANSWER ON THE ATTACHED SHEET MCQ CH.4 . . . . . . . . . . :‫ﺍﻟﺮﻗﻢ ﺍﳉﺎﻣﻌﻲ‬ . . . . . . . . . . . . . . . . . . . . . . :‫ﺍﻻﺳــﻢ‬ ANSWER SHEET 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Dr. Abdallah M. Azzeer Page 6 of 6