Express the sentence in terms of a scalar multiplication of a vector,
A boat is travelling at 25km/h northbound. It turns around and travels at
5km/h southbound.
v = 25j
u = -1/5 v
To express the sentence in terms of a scalar multiplication of a vector, we can assign a vector to represent the boat's motion.
Let's represent the boat's motion as a vector in two dimensions, with northward direction being the positive y-axis and eastward direction being the positive x-axis.
The initial motion of the boat can be represented by a vector [0, 25] km/h, indicating that the boat is travelling at 25 km/h in the positive y-axis direction (northbound).
When the boat turns around, it starts travelling in the opposite direction. So, we can represent the new motion of the boat as a vector [0, -5] km/h, indicating that the boat is travelling at 5 km/h in the negative y-axis direction (southbound).
Therefore, the sentence "A boat is travelling at 25km/h northbound. It turns around and travels at 5km/h southbound." can be expressed in terms of a scalar multiplication of a vector as:
Initial motion: [0, 25] km/h
Turned motion: [0, -5] km/h
To express the sentence in terms of a scalar multiplication of a vector, we need to represent the directions (northbound and southbound) using vectors and the speed (25km/h and 5km/h) as scalar values.
Let's define a vector v1 to represent the boat's initial direction and speed. Since it is traveling northbound at 25km/h, we can represent it as:
v1 = 25 km/h * [0, 1]
Here, [0, 1] represents the unit vector pointing in the northbound direction.
Next, let's define a vector v2 to represent the boat's second direction and speed. Since it is traveling southbound at 5km/h, we can represent it as:
v2 = 5 km/h * [0, -1]
Here, [0, -1] represents the unit vector pointing in the southbound direction.
Now, we can express the sentence in terms of scalar multiplication of vectors as:
A boat is traveling at 25 km/h northbound and then turns around to travel at 5 km/h southbound, which can be represented as:
v1 - v2 = 25 km/h * [0, 1] - 5 km/h * [0, -1]
Simplifying this expression, we get:
v1 - v2 = 25 km/h * [0, 1] + 5 km/h * [0, 1]
= (25 + 5) km/h * [0, 1]
= 30 km/h * [0, 1]
So, we can represent the boat's combined motion as:
v = 30 km/h * [0, 1]
Therefore, the sentence "A boat is traveling at 25km/h northbound. It turns around and travels at 5km/h southbound" can be expressed in terms of a scalar multiplication of a vector as:
v = 30 km/h * [0, 1]