<em><u>Answer:</u></em>
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<em><u>Resultant velocity is the vector sum of all given individual velocities. Velocity is a vector because it has both speed and direction. There are many ways to calculate vector sums, such as using a vector addition diagram, but using trigonometry to calculate vector components is usually more efficient.</u></em>
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Answer:
371.2 mm
Explanation:
The Balmer series of spectral lines is obtained from the formula
1/λ = R(1/2² -1/n²) where λ = wavelength, R = Rydberg's constant = 1.097 × 10⁷ m⁻¹
when n = 15
1/λ = 1.097 × 10⁷ m⁻¹(1/2² -1/15²)
= 1.097 × 10⁷ m⁻¹(1/4 -1/225)
= 1.097 × 10⁷ m⁻¹(0.25 - 0.0044)
= 1.097 × 10⁷ m⁻¹ 0.245556
= 2.693 10⁶ m⁻¹
So,
λ = 1/2.693 10⁶ m⁻¹
= 0.3712 10⁻⁶ m
= 371.2 mm
Answer:
Approximately 
(assuming that the acceleration due to gravity is 
.)
Explanation:
Let 
denote the first piston's contact area with the fluid. Let 
denote the second piston's contact area with the fluid.
Similarly, let 
and 
denote the size of the force on the two pistons. Since the person is placing all her weight on the first piston:
.
Since both pistons fit into cylinders, the two contact surfaces must be circles. Keep in mind that the area of a square is equal to 
times its radius, squared:
.
.
By Pascal's Law, the pressure on the two pistons should be the same. Pressure is the size of normal force per unit area:
.
For the pressures on the two pistons to match:
.
, , and have all been found. The question is asking for . Rearrange this equation to obtain:
.
Evaluate this expression to obtain the value of , which represents the force on the piston with the larger diameter:
.
Answer:
Negative, because the speed is decreasing.
