Friction pushes her hands!!
Answer:
Explanation:
magnetic filed, B = 0.65 T
initial diameter, d = 17.5 cm
final diameter, d' = 6.6 cm
time, t = 0.48 s
(a) According to Lenz's law, the direction of induced current is clockwise.
(b) Let e is the induced emf.
initial area, A = π r² = 3.14 x 0.0875 x 0.0875 = 0.024 m²
final area, A' = π r'² = 3.14 x 0.033 x 0.033 = 0.00342 m²
change in area, ΔA = A - A' = 0.024 - 0.00342 = 0.02058 m²
The magnitude of induced emf is given by
e = 0.65 x 0.02058 / 0.48
e = 0.028 V
(c) R = 2.5 ohm
i = e / R
i = 0.028 / 2.5
i = 0.011 A
Construct a vector diagram. It will be a right-angled triangle. One vector (the hypotenuse) represents the heading of the boat, one represents the current and one represents the resultant speed of the boat, which I'll call x. Their magnitudes are 20, 3 and x. Let the required angle = theta. We have:
<span>theta = arcsin(3/20) = approx. 8.63° </span>
<span>The boat should head against the current in a direction approx. 8.63° to the line connecting the dock with the point opposite, or approx. 81.37° to the shore line. </span>
<span>x = sqrt(20^2 - 3^2) </span>
<span>= sqrt(400 - 9) </span>
<span>= sqrt 391 </span>
<span>The boat's crossing time = </span>
<span>0.5 km/(sqrt 391 km/hr) </span>
<span>= (0.5/sqrt 391) hr </span>
<span>= approx. 0.025 hr </span>
<span>= approx. 91 seconds</span>
The time the package travels horizontally is equal to the time it takes to hit the ground. This can be calculated using:
s = ut + 1/2 at²; u is 0
480 = 4.9t²
t = 9.90 seconds
Horizontal distance = horizontal speed x time
The speed will be converted to m/s from km/h
= 180 km/hr x 1000m/km x 1hr/3600 seconds x 9.90 seconds
= 495 m
