BOAT ACROSS THE RIVER Grade 11 Mathematics project

Boat across the river  Task 1. Task 1.  Task 2. Task 2.  Task 3. Task 3.  Task 4. Task 4.  Task 5. Task 5.  Task6. Task6.

Task 1  Students will search the web to find real life examples on working with vectors, e.g, adding force projectile, components, vectors in 3D, etc.. The common use of vectors involves finding the actual speed and direction of an aircraft given its air speed and direction and the speed and direction of a tailwind. Also to find the angle between the airfield runway and the plane for safe lending. Back

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 velocity. Magnitude Direction = √(10) 2 +(5) 2 = tan -1 = 5/10 = 5√5 units = 26.5 = 27 Back

Task 3  Two horses are pulling the boat along a canal. One horse exerts a force of 300N at an angle 20 and the other 500 N at angle 30. Find the magnitude of the resultant force ? H x1 = 300cos(20) = 281.9N H x2 = 500cos(30)= 433.o1N H y1 = 300 sin(20) = N H y2 = 500sin(30) = 250 N H 1+ H 2 = Magnitude =√( ) 2 +(352.6) 2 = units Back

Task 4  The boat is part of delivering company, it can hold 1200 kg & it capacity is 7.20 cubic meter.the service handles two types of boxes :small, which weight is up to 20 kg & no more than 1200cm 3 & large which 25 kg each & 1600 cm 3 each. The delivery service charges 10 Dhs for small packages and 15 for each large packages. a. write an inequality to represent the weight of the packages in Kg the boat can hold ? 20 x + 25 y ≤ 1200 a. write an inequality to represent the volume in cubic meter of packages the boat can hold ? 2.7m 3 x 100 = 720 cm x y ≤ 720 Back

c. Graph the system of inequality

 d. write a function that represent the amount of money the delivery service will make on each boat hold. P(x,y) = 10x + 15y  e. Find the number of each type of the boxes that should be placed on a boat to maximize revenue. P( 0,0.45) = 10(0)+15(0.45) = $6.7 P(0.6,0) = 10(0.6) + 15(0) = $6

 f. what is the maximum revenue per boat ? $6.7

Task 5  suppose that the force acting on the boat can expressed by vector where each measure in the ordered triple represents the force in Newton. What is the magnitude of the force ? Magnitude = √(45) 2 +(24) 2 +(110) 2 = units Back

Task 6  workers are using a force of 200 N to push a cart up a ramp. The ramp is 6 feet long and is at 30 angle with the horizontal. How much work the workers doing in the vertical direction? you may use sine ratio & formula W= F.d W=Fd Cos = 200 (6) cos (30) = N Back

Done By  Noura Hassan  Alanood Hamad Class :  11.54

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