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Boat across the River Math. (ES) Project

Boat across the River Math. (ES) Project. MOHAMED AHMED ALHEBSI 11-4 MOHAMED KALED 11-4 AHMED OBAID SAEED ALMEHAIRI 11-4 RASHED SAEED RASHED ALHEBSI 11-3. Task 1:.

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Boat across the River Math. (ES) Project

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  1. Boat across the RiverMath. (ES) Project MOHAMED AHMED ALHEBSI 11-4 MOHAMED KALED 11-4 AHMED OBAID SAEED ALMEHAIRI 11-4 RASHED SAEED RASHED ALHEBSI 11-3

  2. Task 1: Students will search the web to find real life examples on working with vectors, e.g. adding forces, projectile, components, vectors in 3D. You could consider throwing a discus or javelin, a hockey bank shot off the boards, football (soccer) ball dynamics, airplane course and speed through the air with wind (like the boat problem, really), playing pool or billiards, the course and speed a baseball fielder must go to intercept the fly ball, and even the course and speed an interceptor must fly to meet an airliner that has been hijacked.

  3. Task 2: If the boat is heading due north as it crosses a river with velocity of 10 km/h relative to water, the river has a uniform velocity of 5 km/h due to east. Graph the vectors in the chart below. Then determine the magnitude and direction of the boat’s velocity. a. R2= V12+V22 √R2= √(10)2+(5)2 R= √100+25 R= √125 R= 5√5 b. θ= tan-1(y÷x) θ= tan-1(10÷5) θ= 63o

  4. Two horses are pulling the boat along a canal, one horse exerts a force of 300 N at an angle20°, and the other exerts 500 N at angle 30°. Find the magnitude of the resultant force. • X-component= -714.9 N • Y-component= 147.4 N • R= √(-714.9)2 + (147.4)2 = 730 N Task 3

  5. Task 4 • The boat is part of delivering company, it can hold 1200 kg and its capacity is 7.20 cubic meter. The service handles two types of boxes: small, which weight is up to 20 kg and no more than 1200 cm3, and large which 25 kg each and 1600 cm3each. The delivery service charges 10Dhs for each small package, and 15 for each large package.

  6. Task 4: • Write an inequality to represent the weight of the packages in kg the boat can hold. Weight: 20kg x + 25kg y ≥1200 kg

  7. Task 4: b. Write an inequality to represent the volume in cubic meter of packages the boat can hold. Capacity: 0.0012x m3+ 0.0016 m3 y ≥ 7.2 m3

  8. Task 4: • 20kg x + 25kg y ≥ 1200 kg • 0.0012x m3 + 0.0016 m3 y ≥ 7.2 m3

  9. Task 4: c. Graph the system of inequality

  10. W`SSSSSSSSS5

  11. Task 4: d. Write a function that represents the amount of money the delivery service will make on each boathold. Coast: 10 Dhs + 15 Dhs= f ( x , y )

  12. Task 4: e. Find the number of each type of the boxes that should be placed on a boat to maximize revenue. 10 Dhs x + 15 Dhs y = f ( 0 , 48 )= 720 Dhs 10 Dhsx + 15 Dhs y = f ( 0 , 0) = 0 10 Dhs x + 15 Dhs y = f ( 60 , 0 ) = 600 Dhs

  13. Task 4: f. What is the maximum revenue per boat? 10 Dhs x + 15 Dhs y = f ( 0 , 48 )= 720 Dhs

  14. Task 5: • Suppose that the force acting on the boat can be expressed by vector <45,24,110> where each measure in the ordered triple represents the force in Newton. What is the magnitude of the force? √452+242+1102= 112.25

  15. Task 6: • Workers are using a force of 200 Newton to push a cart up a ramp. The ramp is 6 feet long and is at 30° angle with the horizontal. How much work are the workers doing in the vertical direction? W= f.dcosθ d=1.8288 m f= 200 N θ= 30° • W= f×d×cosθ • W= (200)(1.8288)cos30° • W= 317 J

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