A hill is 132 m long and makes an angle of 12.0 degrees with the horizontal. As a 54 kg jogger runs up the hill, how much work d

The Pythagorean Theorem can be utilized here: Imagine a car navigating through traffic—when it turns left to travel north, a right angle of 90 degrees is formed. However, the displacement is always the shortest distance connecting the origin and the endpoint, which forms a triangle in this scenario. In a right triangle, the Pythagorean theorem applies: 215^2+45^2=c^2; therefore, v=√(215^2+45^2).

Explanation:

Efficiency can be expressed as the ratio of useful output to the total power consumed.

The fan delivers 500W as useful output while wasting 300W. Thus, the overall power consumed equals 800W (500 + 300).

Answer:

a) factor

b) factor

c) factor

d) factor

Explanation:

For an oscillating spring-mass system, the time period is expressed as:

where:

represents the frequency of oscillation

signifies the mass linked to the spring

is the spring's stiffness constant

a) If the mass is doubled:

• New mass,

Thus, the new time period:

this leads to factor as per the question.

b) When the stiffness constant is quadrupled, holding other factors constant:

New stiffness constant,

Thus, the new time period:

this results in factor as required.

c) When both mass and stiffness constant are quadrupled:

New stiffness,

New mass,

Thus, the new time period:

which leads to factor as stated in the question.

d) If amplitude is quadrupled, the time period remains unaffected because T does not depend on amplitude as demonstrated by the equation.

Thus, factor

The rise in fluid level is 0.11 m, and for mercury, it is 0.728 cm or 7.28 mm. \nTo solve this, here’s the information we have: \n- Density of oil: [density value] \n- Change in pressure in the tank: [pressure change] \n- Density of mercury: [density value] \nTo find the fluid level rise in the manometer: \n1 mmHg equals 133.332 Pa. \nBased on the variables: g is the acceleration due to gravity and h represents the height of the fluid level. \nh = 0.11 m. \nUsing mercury, we find: \nh = 0.00728 m, which is 7.28 mm.