Note: <em>The question states the time to go upstream is a number of times (not explicitly written) the time to go downstream. We'll assume a general number N</em>
Answer:
Explanation:
<u>Relative Speed</u>
If a boat is going upstream against the water current, the true speed of motion is 
, being 
the speed of the boat and 
the speed of the water. If the boat is going downstream, the true speed becomes 
.
The question states the time to go upstream is a number of times N (not explicitly written) the time to go downstream. The speed of an object is computed as
Where x is the distance traveled and t the time taken for that. The time can be computed by
If 
is the time for the upstream travel and 
is the time for the downstream travel, then
Siince the same distance x= 10 miles is traveled in both cases:
Simplifying and rearrangling
Operating
Solving for
If N=3
We can use the required value of N to compute the speed of the boat as explained
Answer:
a = 0.009 J
b = 0.19 m/s
c = 0.005 J and 0.004 J
Explanation:
Given that
Mass of the object, m = 0.5 kg
Spring constant of the spring, k = 20 N/m
Amplitude of the motion, A = 3 cm = 0.03 m
Displacement of the system, x = 2 cm = 0.02 m
a
Total energy of the system, E =
E = 1/2 * k * A²
E = 1/2 * 20 * 0.03²
E = 10 * 0.0009
E = 0.009 J
b
E = 1/2 * k * A² = 1/2 * m * v(max)²
1/2 * m * v(max)² = 0.009
1/2 * 0.5 * v(max)² = 0.009
v(max)² = 0.009 * 2/0.5
v(max)² = 0.018 / 0.5
v(max)² = 0.036
v(max) = √0.036
v(max) = 0.19 m/s
c
V = ±√[(k/m) * (A² - x²)]
V = ±√[(20/0.5) * (0.03² - 0.02²)]
V = ±√(40 * 0.0005)
V = ±√0.02
V = ±0.141 m/s
Kinetic Energy, K = 1/2 * m * v²
K = 1/2 * 0.5 * 0.141²
K = 1/4 * 0.02
K = 0.005 J
Potential Energy, P = 1/2 * k * x²
P = 1/2 * 20 * 0.02²
P = 10 * 0.0004
P = 0.004 J
Answer: The correct answer is : From the period-luminosity relation for Cepheids, he was able to determine the distance to Andromeda and show that it was far outside the Milky Way Galaxy.
Explanation: Hubble's law says that the recession velocity of a galaxy is directly proportional to its distance from us. Hubble measured the distance to the Andromeda galaxy by applying the period-luminosity relationship to Cepheid.
I'm not sure what you're asking but the earth has the ability to infinitely continue to spin or the earth completes 365.25 rotations during a full cycle.
