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Workshop Activity-Electric Boat
Electric Boat
The Problem
A boat rental company on Lake Kerkini is testing a new electric boat.[br]The energy consumption of the boat depends on its speed.[br]From testing, engineers found that the total energy required (in kWh) to travel a fixed distance of 10 km is given by:[math]E\left(x\right)=0.2x^2-1.4x+4.8[/math][br]Where: [list][*][i][size=85]E(x)[/size][/i]: energy (kWh)[/*][*][i]x[/i]: speed (km/h), with ([i] x>3[/i])[/*][/list]
Objective
The owner wants the boat to consume exactly [b]3.6 [/b][b]kWh[/b] for the 10 km route, in order to save battery without moving too slowly.[br]Find the speed(s) that satisfy this condition.[br][br]
Task 1. Form the Equation
Write the equation that represents the problem.[br][br]
Task 2. Solve the Equation
Solve the equation to find the possible values of speed ([i]x[/i])
Task 3. Interpret the Results
[list][*]How many solutions did you find?[/*][*]Which solution makes sense in the context of this problem? [/*][/list]
Aditional Challenge
The boat battery has:[list][*]Voltage: 48 V[/*][*]Capacity: 150 Ah [/*][/list][list=1]Calculate the total energy of the battery (in kWh).[/list]
If the boat battery has Voltage: 48 V and Capacity: 150 Ah, answer the following question:
How many 10 km trips can the boat complete using the energy found above?
Plot the function E(x) and draw the line y = 3.6
Intersection points of E(x) and y=3.6
Find the intersection points.[br]What do these points represent?[br]Which solution would YOU choose as an engineer?