Response:
The new resistance is half of the original resistance.
Explanation:
Resistance in a wire is represented by:
= resistivity of the material
L and A are the physical dimensions
If a wire is exchanged for one where all linear dimensions are doubled, i.e. l' = 2l and r' = 2r
The updated resistance of the wire can be calculated as follows:
The new resistance equals half of the original resistance. Thus, this provides the solution needed.
A. The horizontal component of velocity is
vx = dx/dt = π - 4πsin(4πt + π/2)
vx = π - 4πsin(0 + π/2)
vx = π - 4π(1)
vx = -3π
b. vy = 4πcos(4πt + π/2)
vy = 0
c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]
d. m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]
e. t = -1.0
f. t = -0.35
g. To find t, set
vx = π - 4πsin(4πt + π/2) = 0
Then use this to calculate vxmax
h. To determine t, set
vy = 4πcos(4πt + π/2) = 0
Then use this to find vymax
i. s(t) = [x(t)^2 + y(t)^2]^(1/2)
h. s'(t) = d[x(t)^2 + y(t)^2]^(1/2) / dt
k and l. Determine the values for t
d[x(t)^2 + y(t)^2]^(1/2) / dt = 0
And substitute to find both the maximum and minimum speeds.
Answer:
Explanation:
The overall energy expenditure of the salmon, which corresponds to its swimming upstream effort, 
, is linked to its specific mechanical power. 
calculated per unit mass can be derived from the following equation:
As a result, the total energy utilized during the 22-day journey is 7.603 MJ
d. at the same velocity. Explanation: I'll assume the car is also moving west since the helicopter is stated to be above it. From the perspective of someone in the car, the helicopter will appear stationary as they share the same velocity. Viewed from along the roadside, both are traveling at the same speed. Remember that velocity is a vector quantity, which includes direction, while speed measures the rate at which an object covers distance without direction. Hence, velocity is the appropriate term here.
The greatest mass that can hang without submerging is 2.93 kg. The provided details are as follows: sphere diameter = 20 cm, hence the radius r = 10 cm = 0.10 m. The density of the Styrofoam sphere is 300 kg/m³. The sphere's volume calculates to 4.18 * 10⁻³ m³. Mass M = Density * Volume results in (300)(4.18 * 10⁻³ m³) = 1.25 kg. The displaced water mass is computed as volume * water density, yielding 4.18 * 10⁻³ m³ * 1000 = 4.18 kg. The additional mass the sphere can hold is the difference between the two mass calculations: 4.18 kg - 1.25 kg = 2.93 kg.
