Answer:
(a) θ = 33.86°
(b) Ay = 49.92 N
Explanation:
You have that the magnitude of a vector is A = 89.6 N
The x component of such a vector is Ax = 74.4 N
(a) To find the angle between the vector and the x axis you use the following formula for the calculation of the x component of a vector:
(1)
Ax: x component of vector A
A: magnitude of vector A
θ: angle between vector A and the x axis
You solve the equation (1) for θ, by using the inverse of cosine function:
the angle between the A vector and the x axis is 33.86°
(b) The y component of the vector is given by:
the y comonent of the vecor is Ay = 49.92 N
Answer:
The rate of change of the shadow length of a person is 2.692 ft/s
Solution:
As per the question:
Height of a person, H = 20 ft
Height of a person, h = 7 ft
Rate = 5 ft/s
Now,
From Fig.1:
b = person's distance from the lamp post
a = shadow length
Also, from the similarity of the triangles, we can write:
Differentiating the above eqn w.r.t t:
Now, we know that:
Rate =
Thus
This is an incomplete question, here is a complete question.
The air in the cylinder with a piston has a volume of 220 mL and a pressure of 650 mmHg.
If the pressure inside the cylinder increases to 1.6 atm, what is the final volume, in milliliters, of the cylinder?
Answer : The final volume of the cylinder is, 117.6 mL
Explanation :
Boyle's Law : It is defined as the pressure of the gas is inversely proportional to the volume of the gas at constant temperature and number of moles.
or,
where,
= initial pressure of gas = 650 mmHg = 0.855 atm (1 atm = 760 mmHg)
= final pressure of gas = 1.6 atm
= initial volume of gas = 220 mL
= final volume of gas = ?
Now put all the given values in the above equation, we get:
Therefore, the final volume of the cylinder is, 117.6 mL