Answer:
specifically 30º west of the north
Explanation:
This exercise can be solved using the composition of vectors, let's call the speed of the river that goes east (v₁ = 8 mi / h) to the speed of the boat (v₂ = 16 mi / h) and the desired speed from south to north (v₃ =?). Look at the attachment to be clear about the vectors
Let's use the Pythagorean triangle
v₃² = v₁² + v₂²
Let's calculate v₂
v₂² = v₃² - v₁²
v₂ = √ (16² - 8²)
v₂ = 13.86 mi / h
To find the angle we use trigonometry
sin θ = v1 / v3
θ = sin⁻¹ (v1 / v3)
θ = sin⁻¹ (8/16)
θ = 30º
The boat must be pointed at 30º with respect to the south-north direction, specifically 30º west of the north
First of all, not to get confused with terminology, unit vectors are called unit vectors because they have a unit length. This has absolutely nothing to do with physical units.
Now, if you are talking about physical units like m, m/s or N. Then it depends on what physical vector quantity you’re talking about. If it’s the displacement vector then the i,j,k will have units of length i.e. meters (m). If it’s the force vector then the i,j,k will have units of force i.e. newtons (N).
But if you are talking about vectors in math, then they are unitless. So, we just pretend the physical unit is 1.
Again stressing that this has nothing to do with their name “unit vectors”. They are called that because the unit, AKA the number “1”, is the value of their magnitude/length.
They have magnitude 1, bearing the unit of physical quantity they represent.
Answer:
20600N
Explanation:
Given parameters:
Mass of the roller coaster = 515kg
radius = 10m
Speed = 20m/s
Unknown:
Force of the track pushing up on the vehicle = ?
Solution:
The force pulling the roller coaster along the track is the centripetal force.
To find the centripetal force, use the expression below;
F =
where;
m is the mass
v is the speed
r is the radius
Now insert the parameters and solve;
F = = 20600N
We have that The net force acting on the table is
Fn=14N
From the question we are told
tom and huck are pulling a table in the same direction at the same time with 7N of force each,what is the net force acting on the table
Generally the equation for the Net Force is mathematically given as
Fn=Toms Force +Hucks Force
Therefore
Fn=7+7
Fn=14N
In conclusion
The net force acting on the table is
Fn=14N
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