Start 100 m A person going for a walk follows the path shown in Figure. The tota

Question

Start 100 m A person going for a walk follows the path shown in Figure. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? 1. 300 m End 200 m 150 m 2. (a) Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be larger than the magnitude of A - B by the factor n, what must be the angle between them? (b) What must be the value of the angle between the vectors if the value of n is 100? Children playing in a playground on the flat roof of a city school lose their ball to the parking lot below. One of the teachers kicks the ball back up to the children as shown in the figure below. The playground is 5.80 m above the parking lot, and the school building's vertical wall is h - 7.20 m high, forming a 1.40 m high railing around the playground. The ball is launched at an angle of 6 -53.0° above the horizontal at a point d - 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall (a) Find the speed (in m/s) at which the ball was launched. (b) Find the vertical distance (in m) by which the ball clears the wall (c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball 3. lands.

Explanation / Answer

1.

Suppose given that Vector is R and it makes angle A with +x-axis, then it's components are given by:

Rx = R*cos A

Ry = R*sin A

Using above rule:

R1 = 100 m & angle = 0 deg with +ve x-axis

R1x = R1*cos A1 = 100*cos 0 deg = 100

R1x = 100

R1y = R1*sin A1 = 100*sin 0

R1y = 0

R2 = 300 m & angle = -90 deg with +x-axis

R2x = R2*cos A2 = 300*cos -90 deg

R2x = 0 m

R2y = R2*sin A2 = 300*sin (-90 deg)

R2y = -300 m

R3 = 150 m & angle = 30 deg below -ve x-axis

R3x = R3*cos A3 = -150*cos 30 deg

R3x = -129.90 m

R3y = R3*sin A3 = -150*sin 30 deg

R3y = -75 m

R4 = 200 m & angle = 60 deg above -ve x-axis

R4x = R3*cos A3 = -200*cos 60 deg

R4x = -100 m

R4y = R3*sin A3 = 200*sin 60 deg

R4y = 173.20 m

Now

Rnet = Rnet)x + Rnet)y

Rnet = (R1x + R2x + R3x + R4x) i + (R1y + R2y + R3y + R4y) j

Using above values

Rnet = (100 + 0 - 129.90 - 100) i + (0 - 300 - 75 + 173.20) j

Rnet = -129.90 i - 201.8 j

|Rnet| = sqrt (Rnet_x^2 + Rnet_y^2)

|Rnet| = sqrt ((-129.90)^2 + (-201.8)^2)

|Rnet| = 239.99 m = 240 m

Direction of Rnet will be

Direction = arctan (Rnet_y/Rnet_x)

Direction = arctan (201.8/129.90) = 57.23 deg

Direction = 57.23 deg below negative x-axis = 180 + 57.23 = 237.23 deg CCW from +ve x-axis

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