Answer: Hello mate!
lets define the north as the y-axis and east as the x-axis.
Using the notation (x,y) we can define the initial position of the car as (0,0)
then the car travells 13 mi east, so now the position is (13,0)
then the car travels Y miles to the north, so the position now is (13, Y)
and we know that the final position is 25° degrees north of east of the initial position. This angle says that the distance traveled to the north is less than 13 mi because this angle is closer to the x-axis (or east in this case).
This angle is measured from east to north, then the adjacent cathetus is on the x-axis, in this case, 13mi
And we want to find the distance Y, so we can use the tangent:
Tan(25°) = Y/13
tan(25°)*13 mi = Y = 6.06 mi.

The apparent depth of an object at the bottom of a tank filled with a liquid of refractive index 1.3 is 7.7 cm. What is the actual depth of the liquid in the tank?

REFRACTIVE INDEX = 1.3
APPARENT DEPTH = 7.7 cm

REAL DEPTH OF THE OBJECT.



Refractive Index = 1.3
Apparent Depth = 7.7 cm
Putting the values in the formula:-

Answer:
Part a)

Part b)
Since the radius is decreasing so induced current will increase the flux through the coil
So it would be clockwise in direction
Explanation:
As we know that magnetic flux linked with the coil is given as

now the rate of change in flux is given as

now we know that circumference is decreasing at rate of 15 cm/s
so here we know the length of circumference as

So rate of change in circumference is


final length of circumference at t = 8 s

Part a)
Now the induced EMF is given as



Part b)
Since the radius is decreasing so induced current will increase the flux through the coil
So it would be clockwise in direction