BOAT ACROSS THE RIVER

Grade 11 Mathematics project

Boat across the river

Task 1. Task 2. Task 3. Task 4. Task 5. 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.

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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

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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 ?

Hx1 = 300cos(20) = 281.9N Hx2 = 500cos(30)= 433.o1N

Hy1 = 300 sin(20) = 102.6 N Hy2 = 500sin(30) = 250 N

H1+H2 < 281.9+433.01,102.6+350> = < 714.91 , 352.6 >

Magnitude

=√(714.011)2+(352.6)2 = 797.13 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 1200cm3 & large which 25 kg each & 1600 cm3 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 ?

2.7m3 x 100 = 720 cm3

1200x + 1600 y ≤ 720

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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 <45,24,110> 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

= 121.247 units

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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)

= 1039.23 N

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Done By

Noura Hassan Alanood Hamad

Class : 11.54

http://meenowh.wikispaces.com