Answer: a) Twice Chuck's
Explanation:
If the angular speed is constant, as the merry - go -round is a rigid body, so the distance between two points must remain the same, it is needed that the points farther the center, move faster than the ones closer to it.
There exists a relationship between tangential and angular speed, as follows, that relates the definitions of linear and angular speed, and the angle definition:
angle = arc / radius ⇒ Δθ/Δt = Δs/Δt / r ⇒ ω = v/r ⇒ v = ω. r
If ω is constant, v is directly proportional to r, distance to the center (radius in a circular platform), so if r is twice for Andrea, her tangential speed must be twice Chuck's.
Answer:
1) 
2) 
3) 

Explanation:
Given:
width of river, 
speed of stream with respect to the ground, 
speed of the swimmer with respect to water, 
<u>Now the resultant of the two velocities perpendicular to each other:</u>



<u>Now the angle of the resultant velocity form the vertical:</u>



- Now the distance swam by the swimmer in this direction be d.
so,



Now the distance swept downward:



2)
On swimming 37° upstream:
<u>The velocity component of stream cancelled by the swimmer:</u>



<u>Now the net effective speed of stream sweeping the swimmer:</u>



<u>The component of swimmer's velocity heading directly towards the opposite bank:</u>



<u>Now the angle of the resultant velocity of the swimmer from the normal to the stream</u>:



- Now let the distance swam in this direction be d'.



<u>Now the distance swept downstream:</u>



3)
Time taken in crossing the rive in case 1:



Time taken in crossing the rive in case 2:



Answer:
the greatest number of protons is astatine (At)
(A) We can solve the problem by using Ohm's law, which states:

where
V is the potential difference across the electrical device
I is the current through the device
R is its resistance
For the heater coil in the problem, we know

and

, therefore we can rearrange Ohm's law to find the current through the device:

(B) The resistance of a conductive wire depends on three factors. In fact, it is given by:

where

is the resistivity of the material of the wire
L is the length of the wire
A is the cross-sectional area of the wire
Basically, we see that the longer the wire, the larger its resistance; and the larger the section of the wire, the smaller its resistance.