What are the given choices?
Answer:
specifically 30º west of the north
Explanation:
This exercise can be solved using the composition of vectors, let's call the speed of the river that goes east (v₁ = 8 mi / h) to the speed of the boat (v₂ = 16 mi / h) and the desired speed from south to north (v₃ =?). Look at the attachment to be clear about the vectors
Let's use the Pythagorean triangle
v₃² = v₁² + v₂²
Let's calculate v₂
v₂² = v₃² - v₁²
v₂ = √ (16² - 8²)
v₂ = 13.86 mi / h
To find the angle we use trigonometry
sin θ = v1 / v3
θ = sin⁻¹ (v1 / v3)
θ = sin⁻¹ (8/16)
θ = 30º
The boat must be pointed at 30º with respect to the south-north direction, specifically 30º west of the north
The object with the greater mass should be attached to the spring with the smaller spring constant, so that the resulting spring-object system has the greatest possible period of oscillation.
Answer: Option D
<u>Explanation:
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According to the simple harmonic motions, from physics, it gives a relation between deformation force and the deflection. The more deflection results in more time period of oscillation.
F = - k x
where ‘k’ is the spring constant, and ‘F’ is the deformation force.
So, deflection is directly proportionate to forces, and inversely proportionate to its spring constant. Hence, we can derive that the force must be maximum, and hence weight must be maximum, with the spring constant lesser. Then, the deflection will be high. So, time period increases.
The kinetic energy needed by the man is
Explanation:
The escape velocity (the speed needed by an object in the Earth's surface to escape the Earth's gravitational field) is given by
where
G is the gravitational constant
M is the Earth's mass
R is the radius of the Earth
For the Earth, we have
Substituting, we find the escape velocity:
Now we can find the kinetic energy that the man would need, which is given by
where
m = 65 kg is the mass of the person
is the escape velocity
Substituting,
Learn more about kinetic energy:
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All you would do is for a, 10 times 2 is 20 so it would be 20-dB
For b, 10 times 4 is 40 so it would be 40-dB
For c, 10 times 8 is 80 so it would be 80-dB