Workshop Activity-Electric Boat

Electric Boat

The Problem

A boat rental company on Lake Kerkini is testing a new electric boat. The energy consumption of the boat depends on its speed. From testing, engineers found that the total energy required (in kWh) to travel a fixed distance of 10 km is given by:

Where:

E(x): energy (kWh)
x: speed (km/h), with ( x>3)

Objective

The owner wants the boat to consume exactly 3.6 kWh for the 10 km route, in order to save battery without moving too slowly. Find the speed(s) that satisfy this condition.

Task 1. Form the Equation

Write the equation that represents the problem.

Task 2. Solve the Equation

Solve the equation to find the possible values of speed (x)

Task 3. Interpret the Results

How many solutions did you find?
Which solution makes sense in the context of this problem?

Aditional Challenge

The boat battery has:

Voltage: 48 V
Capacity: 150 Ah

Calculate the total energy of the battery (in kWh).

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. What do these points represent? Which solution would YOU choose as an engineer?