Answer:
The x-component of the electric field at the origin = -11.74 N/C.
The y-component of the electric field at the origin = 97.41 N/C.
Explanation:
<u>Given:</u>
- Charge on first charged particle,

- Charge on the second charged particle,

- Position of the first charge =

- Position of the second charge =

The electric field at a point due to a charge
at a point
distance away is given by

where,
= Coulomb's constant, having value 
= position vector of the point where the electric field is to be found with respect to the position of the charge
.
= unit vector along
.
The electric field at the origin due to first charge is given by

is the position vector of the origin with respect to the position of the first charge.
Assuming,
are the units vectors along x and y axes respectively.

Using these values,

The electric field at the origin due to the second charge is given by

is the position vector of the origin with respect to the position of the second charge.

Using these values,

The net electric field at the origin due to both the charges is given by

Thus,
x-component of the electric field at the origin = -11.74 N/C.
y-component of the electric field at the origin = 97.41 N/C.
Answer:
Explanation:
When the box is on the ramp , component of its weight along the ramp
= mg sinθ
Friction force acting on it in upward direction
=μ mg cosθ
For sliding
μ mg cosθ < mg sinθ
μ cosθ < sinθ
.5 x cos35 < sin35
.41 < .57
So the box will slide
When sliding starts , kinetic friction acts
Net force in downward direction
mgsinθ - μ mg cosθ
acceleration
= gsinθ - μ g cosθ
= 5.62 - .3 x 9.8 x cos35
= 5.62 - 2.4
= 3.22 m /s²
Initial velocity u = 50 miles/hour
acceleration a = 10 miles/hour
Time t = 2 hours
Distance travelled S = ut + (at^2)/2
Substituting the values in the second equation of motion,
S = 50*2 + (10 * 2 *2)/2
S = 100 + 20
S = 120 miles
Therefore the distance travelled by the car in the next two hours is 120 miles
The tank has a volume of
, where
is its height and
is its radius.
At any point, the water filling the tank and the tank itself form a pair of similar triangles (see the attached picture) from which we obtain the following relationship:

The volume of water in the tank at any given time is

and can be expressed as a function of the water level alone:

Implicity differentiating both sides with respect to time
gives

We're told the water level rises at a rate of
at the time when the water level is
, so the net change in the volume of water
can be computed:

The net rate of change in volume is the difference between the rate at which water is pumped into the tank and the rate at which it is leaking out:

We're told the water is leaking out at a rate of
, so we find the rate at which it's being pumped in to be

