Forklift 3 3 7. We can use vectors to solve many problems involving physical quantities such as velocity, speed, weight, work and so on.
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Velocity:
The velocity of moving object is modeled by a vector whose direction is the direction of motion and whose magnitude is the speed.
Example :
A ball is thrown with an initial velocity of 70 feet per second., at an angle of 35 ° Comic life 3 0 – create web ready comic strips. with the horizontal. Find the vertical and horizontal components of the velocity.
Let v represent the velocity and use the given information to write v in unit vector form:
v = 70 ( cos ( 35 ° ) ) i + 70 ( sin ( 35 ° ) ) j
Simplify the scalars, we get:
v ≈ 57.34 i + 40.15 j
Since the scalars are the horizontal and vertical components of v ,
Therefore, the horizontal component is 57.34 feet per second and the vertical component is 40.15 feet per second.
Force:
Force is also represented by vector. If several forces are acting on an object, the resultant force experienced by the object is the vector sum of these forces.
Example :
Two forces F 1 and F 2 with magnitudes 20 and 30 lb , respectively, act on an object at a point P as shown. Find the resultant forces acting at P .
First we write F 1 and F 2 in component form:
v ≈ 57.34 i + 40.15 j
Simplify the scalars, we get:
F 1 = ( 20 cos ( 45 ° ) ) i + ( 20 sin ( 45 ° ) ) j = 20 ( 2 2 ) i + 20 ( 2 2 ) j = 10 2 i + 10 2 j F 2 = ( 30 cos ( 150 ° ) ) i + ( 30 sin ( 150 ° ) ) j = 30 ( − 3 2 ) i + 30 ( 1 2 ) j = − 15 3 i + 15 j
So, the resultant force F is
F = F 1 + F 2 = ( 10 2 i + 10 2 j ) + ( − 15 3 i + 15 j ) = ( 10 2 − 15 3 ) i + ( 10 2 + 15 ) j ≈ − 12 i + 29 j
Work:
Screenflick 2 7 18 download free. The work W done by a force F in moving along a vector D is W = F ⋅ D .
Example :
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A force is given by the vector F = ⟨ 2 , 3 ⟩ and moves an object from the point ( 1 , 3 ) to the point ( 5 , 9 ) . Find the work done.
First we find the Displacement.
The displacement vector is
D = ⟨ 5 − 1 , 9 − 3 ⟩ = ⟨ 4 , 6 ⟩ .
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By using the formula, the work done is
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W = F ⋅ D = ⟨ 2 , 3 ⟩ ⋅ ⟨ 4 , 6 ⟩ = 26
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If the unit of force is pounds and the distance is measured in feet, then the work done is 26 ft-lb.
