Motion in a Plane Test 3

Scalar quantity gives you an idea about how much of an object there is, but vector quantity gives you an indication of how much of an object there is and that also in which direction. So, the main difference between these two quantities is associated with the direction, i.e. scalars do not have direction but vectors do. 

Explanation:An object that falls through a vacuum is subjected to only one external force, the gravitational force, expressed as the weight of the object. An object that is moving only because of the action of gravity is said to be free falling and its motion is described by Newton's second law of motion. With algebra we can solve for the acceleration of a free falling object. The acceleration is constant and equal to the gravitational acceleration g which is 9.8 meters per square second at sea level on the Earth. The weight, size, and shape of the object are not a factor in describing a free fall.

Explanation:The net acceleration of a particle in circular motion is along the radius of the circle towards the centre Only in case of uniform circular motion.

Explanation:if a ball is thrown upward at an angle? The ball has a vertical and a horizontal component of velocity. The force of gravity is acting on it and its acceleration is in the downward direction. The vertical component of velocity is therefore changing. As the motion and acceleration is in opposite direction so vertical component of velocity decrease.

Explanation:Parallelogram law of vector addition is,If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.

Explanation:The sum of two or more vectors is called the resultant. The resultant of two vectors can be found using either the triangle method or the parallelogram method.

Explanation:A particle with a vertical and horizontal velocity travelling in a gravitational field will trace out a parabola.

Explanation:In order to take a safe turn, the cyclist has to bend a little from his vertical position. In this case, a component of the reaction provides the required centripetal force.If q is angle made by the cyclist with the vertical then

In actual practice, the value of q is slightly less because the force of friction also contributes towards the centripetal force.

Explanation:The maximum possible value for displacement is the distance travelled, so it cannot be of a greater value than distance (path length).The magnitude of the displacement is always less than or equal to the distance traveled. If two displacements in the same direction are added, then the magnitude of their sum will be equal to the distance traveled.

Explanation:Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.

Explanation:The motorcycle’s x- and  y-coordinates at t=0.50 s are

The negative value of y shows that the motorcycle is below its starting point.

The motorcycle’s distance from the origin at t=0.50 s is 

Explanation:Equal vectors are vectors that have the same magnitude and the same direction. Equal vectors may start at different positions.

Explanation:Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity about a particular axis.

Explanation:

The car is in uniform circular motion because it’s moving at a constant speed along a curve that is a segment of a circle. Hence we know 

This is the minimum turning radius because arad is the maximum centripetal acceleration.

Radius of the circular path, r = 70m
Time takes to complete one round, t = 11s
Total length of the path, s = 2πr = 2*22/7*70 = 440m

Work is the energy transferred to an object by force. It is a scalar quantity because it's the product of force and displacement. Work is not the same thing as force, which is a vector quantity, because work is the result of force.

Explanation:The flag is fluttering in the north-east direction. It shows that the wind is blowing toward the north-east direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity (vwb) of the wind with respect to the boat.

Hence, the flag will flutter approximately due east.

Explanation:Vector addition is commutative, just like addition of real numbers. If you start from a point say P,  you end up at the same spot no matter which displacement (a or b) you take first. The head-to-tail rule yields vector c for both a + b and b + a.

Explanation:Although vectors and scalars represent different types of physical quantities, it is sometimes necessary for them to interact. While adding a scalar to a vector is impossible because of their different dimensions in space, it is possible to multiply a vector by a scalar.

Explanation:

Speed of the man, v_m = 4 km/h
Width of the river = 1 km

Explanation:

If a vector is multiplied by a scalar as in  pA^→ ,  then the magnitude of the resulting vector is equal to the product of p and the magnitude of  A^→, and its direction is the same as  A^→ if p is positive and opposite to  A^→ if p is negative.

Distributive law for scalar multiplication:

p(A^→ +B^→ )=pA^→ +pB^→ 

Explanation:A displacement is vector that is the shortest path length from the initial to the final position of the body. It is not always eqaul to path length. It can be zero and -ve also.

The described situation is shown in the given figure.

 Here,

v_c = Velocity of the cyclist
v_r = Velocity of falling rain

In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.

Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18° with the vertical.

Explanation:A null vector is a vector having magnitude equal to zero.It is represented by 0^→.A null vector has no direction or it may have any direction.Generally a null vector is either equal to resultant of two equal vectors acting in opposite directions or multiple vectors in different directions.

0^→ =A^→ +(−A^→ )

(b) Distance between the hostel and the station = 10 km = Displacement of the car

∴ Average velocity = 

Explanation:

Initial velocity u = 150 m/s

Explanation:Acceleration is a vector quantity because it has both magnitude and direction.When an object has a positive acceleration, the acceleration occurs in the same direction as the movement of the object.When an object has a negative acceleration (it's slowing down), the acceleration occurs in the opposite direction as the movement of the object.

Explanation:

Vector subtraction is defined in the following way.

• The difference of two vectors, A - B , is a vector C that is, C = A - B
• The addition of two vector such that C = A + (-B). B has been taken in opposite direction.

Thus vector subtraction can be represented as a vector addition.

Explanation:

(i) PQ = diameter = displacement for each girl = 2r = 2 x 200 = 400 m

Since, displacement vector does not depend upon the actual path length and it is the shortest distance between initial and final position, so in the case of each girl the displacement is 400 m.

(ii)This is equal to the actual length of the path skated by girl B.

Explanation:Electric current is a scalar quantity.It represents the direction of flow of positive charge but it is treated as a scalar quantity because current follows the laws of scalar addition and not the laws of vector addition,because the angle between the wires carrying current does not effect the total current in the circuit.