Answer:
a) 43.20V
b) 2.71W/s
c) 40.25s
d) 7.77Nm
Explanation:
(a) The emf of a rotating coil with N turns is given by:

N: turns
B: magnitude of the magnetic field
A: area
w: angular velocity
the emf max is given by:

(b) the maximum rate of change of the magnetic flux is given by:

(c) 
(d) The torque is given by:

Answer:
v = 19.6 m/s.
Explanation:
Given that,
The radius of the circle, r = 5 m
The time period of the ball, T = 1.6s
We need to find the ball's tangential velocity.
The formula for the tangential velocity is given by :

Putting all the values in the above formula

So, the tangential velocity of the ball is 19.6 m/s. Hence, the correct option is (c).
Answer:
0.57 m
Explanation:
First of all, we need to calculate the time it takes for the ball to cover the horizontal distance between the starting position and the crossbar. This can be done by analzying the horizontal motion only. In fact, the horizontal velocity is constant and it is

And the distance to cover is
d = 19 m
So the time taken is

Now we want to find how high the ball is at that time. The initial vertical velocity is

So the vertical position of the ball at time t is

where g = 9.8 m/s^2 is the acceleration of gravity. Substituting t = 2.04 s, we find

The crossbar height is 3.05 m, so the difference is

So the ball passes 0.57 m above the crossbar.
Answer:
4.0 m/s
Explanation:
The motion of the diver is the motion of a projectile: so we need to find the horizontal and the vertical component of the initial velocity.
Let's consider the horizontal motion first. This motion occurs with constant speed, so the distance covered in a time t is

where here we have
d = 3.0 m is the horizontal distance covered
vx is the horizontal velocity
t = 1.3 s is the duration of the fall
Solving for vx,

Now let's consider the vertical motion: this is an accelerated motion with constant acceleration g=9.8 m/s^2 towards the ground. The vertical position at time t is given by

where
h = 4.0 m is the initial height
vy is the initial vertical velocity
We know that at t = 1.3 s, the vertical position is zero: y = 0. Substituting these numbers, we can find vy

So now we can find the magnitude of the initial velocity:
