Answer:
352,088.37888Joules
Explanation:
Complete question;
A hiker of mass 53 kg is going to climb a mountain with elevation 2,574 ft.
A) If the hiker starts climbing at an elevation of 350 ft., what will their change in gravitational potential energy be, in joules, once they reach the top? (Assume the zero of gravitational potential is at sea level)
Chane in potential energy is expressed as;
ΔGPH = mgΔH
m is the mass of the hiker
g is the acceleration due to gravity;
ΔH is the change in height
Given
m = 53kg
g = 9.8m/s²
ΔH = 2574-350 = 2224ft
since 1ft = 0.3048m
2224ft = (2224*0.3048)m = 677.8752m
Required
Gravitational potential energy
Substitute the values into the formula;
ΔGPH = mgΔH
ΔGPH = 53(9.8)(677.8752)
ΔGPH = 352,088.37888Joules
Hence the gravitational potential energy is 352,088.37888Joules
Answer:
a
The number of radians turned by the wheel in 2s is 
b
The angular acceleration is 
Explanation:
The angular velocity is given as

Now generally the integral of angular velocity gives angular displacement
So integrating the equation of angular velocity through the limit 0 to 2 will gives us the angular displacement for 2 sec
This is mathematically evaluated as

![= [\frac{2t^2}{2} + \frac{t^4}{4}] \left\{ 2} \atop {0}} \right.](https://tex.z-dn.net/?f=%3D%20%5B%5Cfrac%7B2t%5E2%7D%7B2%7D%20%2B%20%5Cfrac%7Bt%5E4%7D%7B4%7D%5D%20%5Cleft%5C%7B%202%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
![= [\frac{2(2^2)}{2} + \frac{2^4}{4}] - 0](https://tex.z-dn.net/?f=%3D%20%5B%5Cfrac%7B2%282%5E2%29%7D%7B2%7D%20%2B%20%5Cfrac%7B2%5E4%7D%7B4%7D%5D%20-%200)


Now generally the derivative of angular velocity gives angular acceleration
So the value of the derivative of angular velocity equation at t= 2 gives us the angular acceleration
This is mathematically evaluated as

so at t=2


The amount of current is the same through any component in a series circuit. Resistance: The total resistance of any series circuit is equal to the sum of the individual resistances. Voltage: The supply voltage in a series circuit is equal to the sum of the individual voltage drops.
Answer: h = 0.52m
Explanation:
Using the equation of out flow;
A1 × V1 = A2 ×V2
Where A1 = area of the first nozzle
A2 = area of the second nozzle
V1= velocity of flow out from the first nozzle
V2 = velocity of flow out from 2nd nozzle
But AV= area of nozzle × velocity of water = volume of water per second(m³/s).
Now we can set A×V = Area of nozzle × height of rise.
Henceb A1× h1 = A2 × h2 ( note the time cancel on both sides)
D1 = 20mm= 0.02m; h1 = 0.13m
D2 = 10mm = 0.01m; h2= ?
h2 = π(D1/2)²× h1 /π(D2/2)²
h2 = (0.02/2)² × 0.13/(0.01/2)²
= (0.01)² ×0.13 /(0.005)²
= 1.3 × 10^-5/(5 × 10^-3)²
= 1.3 × 10^-5/25 × 10^-6
= (1.3/25) 10^-5 × 10^6
= 0.052× 10
= 0.52m