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) = $6.7P(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
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