1) Distance: 14 km
2) Speed: 3.5 km/h
3) Displacement: 7.6 km at [tex]23.2^{\circ}[/tex] north of west
4) Velocity: 1.9 km/h at [tex]23.2^{\circ}[/tex] north of west
Explanation:
1)
Distance is a scalar quantity, and it corresponds to the total length of the path covered by an object during its motion, regardless of its direction.
Here we have the following motion:
[tex]d_{y1}=5 km[/tex] North
[tex]d_x = 7 km[/tex] west
[tex]d_{y2}=2 km[/tex] south
So, the distance covered is:
[tex]d=d_x + d_y = 5 + 7 +2 = 14 km[/tex]
And since it is a scalar, distance has no direction.
2)
Speed is a scalar quantity telling "how fast" an object is moving. It is calculated as:
[tex]speed=\frac{d}{t}[/tex]
where:
d is the distance
t is the time taken
In this problem, we have
d = 14 km (distance)
t = 4 h (time taken)
Substituting,
[tex]speed=\frac{14 km}{4 h}=3.5 km/h[/tex]
And since it is a scalar, it has no direction.
3)
Displacement is a vector quantity connecting the initial position to the final position of motion. The magnitude is the short distance in a straight line between the initial and final position of motion.
Here we have the following motions:
[tex]d_{y1}=5 km[/tex] North
[tex]d_x = 7 km[/tex] west
[tex]d_{y2}=2 km[/tex] south
So the net displacement in the north-south direction is
[tex]d_y = 5 - 2 = 3 km[/tex] North
[tex]d_x, d_y[/tex] are at right angle, so they form the sides of a right triangle, of which the hypothenuse corresponds to the displacement. Therefore, we can find the magnitude of the displacement by using Pythagorean's theorem:
[tex]d=\sqrt{d_x^2+d_y^2}=\sqrt{7^2+3^2}=7.6 km[/tex]
And the direction is given by
[tex]\theta=tan^{-1}(\frac{d_y}{d_x})=tan^{-1}(\frac{3}{7})=23.2^{\circ}[/tex] north of west.
4)
Velocity is a vector quantity, given by:
[tex]velocity=\frac{d}{t}[/tex]
where
d is the displacement
t is the time taken
In this problem, we have
d = 7.6 km (displacement)
t = 4 h (time taken)
So, the velocity is
[tex]velocity=\frac{7.6 km}{4h}=1.9 km/h[/tex]
And being a vector, velocity has also a direction, which is the same of the displacement: so, [tex]23.2^{\circ}[/tex] north of west.
Learn more about distance and displacement:
brainly.com/question/3969582
Learn more about speed and velocity:
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