Answer:
Rate of change of area will be
Explanation:
We have given rate of change of radius
Radius of the circular plate r = 52 cm
Area is given by
So
Puting the value of r and
So rate of change of area will be
Scientists are studying a moving glacier. To monitor the flow of the glacier, they place a series of five markers, A, B, C, D, a
1 answer:
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Answer:
The rock must leave the cliff at a velocity of 28.2 m/s
Explanation:
The position vector of the rock at a time t can be calculated using the following equation:
r = (x0 + v0x · t, y0 + 1/2 · g · t²)
Where:
r = position vector at time t.
x0 = initial horizontal position.
v0x = initial horizontal velocity.
t = time.
g = acceleration due to gravity (-9.81 m/s² considering the upward direction as positive).
Please, see the attached figure for a graphical description of the problem. Notice that the origin of the frame of reference is located at the edge of the cliff so that x0 and y0 = 0.
When the rock reaches the ground, the position vector will be (see r1 in the figure):
r1 = (90 m, -50 m)
Then, using the equation of the vector position written above:
90 m = x0 + v0x · t
-50 m = y0 + 1/2 · g · t²
Since x0 and y0 = 0:
90 m = v0x · t
-50 m = 1/2 · g · t²
Let´s use the equation of the y-component of the vector r1 to find the time it takes the rock to reach the ground and with that time we can calculate v0x:
-50 m = 1/2 · g · t²
-50 m = -1/2 · 9.81 m/s² · t²
-50 m / -1/2 · 9.81 m/s² = t²
t = 3.19 s
Now, using the equation of the x-component of r1:
90 m = v0x · t
90 m = v0x · 3.19 s
v0x = 90 m / 3.19 s
v0x = 28.2 m/s
Answer:
V1 = 2221.33 L
Explanation:
The system is about a ideal gas. Then you can use the equation for ideal gases for a volume V1, temperature T1 and pressure P1:
(1)
And also for the situation in which the variables T, V and P has changed:
(1)
R: constant of ideal gases = 0.082 L.atm/mol.K
For both cases (1) and (2) the number of moles are the same. Next, you solve for n in (1) and (2):
Next, you equal these equations an solve for T2:
Finally you replace the values of P2, V2, T1 and T2:
Hence, the initial volume of the gas is 2221.33 L