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Pi] A car's engine produces a useful output power of 6.5 10° W
The car of mass 950 kg is moving up a hill at a steady speed.
The slope of the hill is 12° to the horizontal. Resistive forces on the car are negligible.
1?
What is the steady speed of the car? rk
[1 mark]
A 7.0ms7 [e]
B 12ms7 [e]
Cc 34ms7 [=]
D 68ms7 [e]

Pi A cars engine produces a useful output power of 65 10 W The car of mass 950 kg is moving up a hill at a steady speed The slope of the hill is 12 to the horiz class=

Respuesta :

LammettHash

Recall that

P = F v

where

P = power produced by the engine

F = magnitude of the component force supplied by the engine in the direction of the car's motion

v = speed of the car

Draw a free-body diagram for the car, and decompose all the forces acting on it into components that act parallel and perpendicular to the slope. The car moves parallel to the slope, so we only care about 2 forces: the parallel component of the car's weight, and the force provided by the engine.

By Newton's second law, since the car is moving at a constant speed,

∑ F = F - m g sin(12°) = 0

where m = 950 kg and g = 9.80 m/s². Solve for F :

F = m g sin(12°) ≈ 1935.658 N

The engine provides P = 6.5 × 10⁴ W, so the car's speed v is

v = P / F = (6.5 × 10⁴ W) / (1935.658 N) ≈ 33.6 m/s

which makes C : 34 ms⁝š the closest answer.

asuwafohjames

The Steady speed of a car moving up a hill, with a slope of 12° to the horizontal,  whose output power is 6.5×10⁴ W and whose mass is 950 kg is A. 7.0 m/s

Speed: This can be defined as the ratio of distance to the time travelled by a body. The S.I unit of speed is m/s

  • The question above can be solved using the formula below

[tex]P = (mgcosx)V[/tex].................... Equation 1

Where P = output Power of the engine, m = mass of the car, g = acceleration due to gravity, x = angle of the hill with the horizontal, V = steady speed of the car.

  • Make V the subject of the equation

[tex]V = P/mgcosx[/tex]............... Equation 2

From the question,

  • Given: P = 6.5×10⁴ W, m = 950 kg, x = 12°                                      Constant: g = 9.8 m/s²
  • Substitute the values into equation 2

[tex]V = (6.5*10^{4} )/(950*9.8*cos12)[/tex]

[tex]V = 65000/9106.55[/tex]

[tex]V = 7.13 m/s[/tex]

From the question, the right option is A. 7.0 m/s

Hence the steady speed of the car is 7.0 m/s

Learn more about speed here: https://brainly.com/question/18316946

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