Answer:
The charge flows in coulombs is

Explanation:
The current magnitude of current is given by the resistance and the induced Emf as:



,
,
,
Ω
,
Replacing :


Answer:
3.25 seconds
Explanation:
It is given that,
A person throws a baseball from height of 7 feet with an initial vertical velocity of 50 feet per second. The equation for his motion is as follows :

Where
s is the height in feet
For the given condition, the equation becomes:

When it hits the ground, h = 0
i.e.

It is a quadratic equation, we find the value of t,
t = 3.25 seconds and t = -0.134 s
Neglecting negative value
Hence, for 3.25 seconds the baseball is in the air before it hits the ground.
Answer:
a) 17.086m
b) 0.1671 m
Explanation:
Given data: speed of water through the hose = 1.81 m/s
through the nozzle = 18.3 m/s
We know that maximum height of an object with upward velocity v is given by,
a) H = v^2/2g
where H is the maximum height water emerges
= 18.3^2/(2×9.8) = 17.086 m answer
b) Again,
H = v^2/2g
= 1.81^2/(2×9.8) = 0.1671 m
Answer:at 21.6 min they were separated by 12 km
Explanation:
We can consider the next diagram
B2------15km/h------->Dock
|
|
B1 at 20km/h
|
|
V
So by the time B1 leaves, being B2 traveling at constant 15km/h and getting to the dock one hour later means it was at 15km from the dock, the other boat, B1 is at a distance at a given time, considering constant speed of 20km/h*t going south, where t is in hours, meanwhile from the dock the B2 is at a distance of (15km-15km/h*t), t=0, when it is 8pm.
Then we have a right triangle and the distance from boat B1 to boat B2, can be measured as the square root of (15-15*t)^2 +(20*t)^2. We are looking for a minimum, then we have to find the derivative with respect to t. This is 5*(25*t-9)/(sqrt(25*t^2-18*t+9)), this derivative is zero at t=9/25=0,36 h = 21.6 min, now to be sure it is a minimum we apply the second derivative criteria that states that if the second derivative at the given critical point is positive it means here we have a minimum, and by calculating the second derivative we find it is 720/(25 t^2 - 18 t + 9)^(3/2) that is positive at t=9/25, then we have our answer. And besides replacing the value of t we get the distance is 12 km.
Answer:
0.775 m
Explanation:
As the car collides with the bumper, all the kinetic energy of the car (K) is converted into elastic potential energy of the bumper (U):

where we have
is the spring constant of the bumper
x is the maximum compression of the bumper
is the mass of the car
is the speed of the car
Solving for x, we find the maximum compression of the spring:
