how to solve numerical in vector
Answers
Answer:
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° 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 ≈57.34i+40.15j
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 F1 and F2 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 F1 and F2 in component form:
v≈57.34i+40.15j
Simplify the scalars, we get:
F1=(20cos(45°))i+(20sin(45°))j=20(2√2)i+20(2√2)j=102√i+102√jF2=(30cos(150°))i+(30sin(150°))j=30(−3√2)i+30(12)j=−153√i+15j
So, the resultant force F is
F=F1+F2=(102√ i+102√j)+(−153√ i+15j)=(102√−153√)i+(102√+15)j≈−12i+29j
Explanation:
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