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swat32
3 years ago
12

A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 4.0º to the hor

izontal. If friction forces are ignored, how far along the hill does she travel before stopping?

Physics
1 answer:
IrinaK [193]3 years ago
6 0
The kinetic energy K = 0.5 * m * v² must be equal to the potential energy U = m * g * h.

m mass
v velocity
h height
g = 9.81m/s²

The mass m cancels out:
0.5 * v² = g * h
Solve for height h and transform to distance traveled.
(sin (4°) = height / distance)

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An earthquake produces longitudinal P waves that travel outward at 8000 m/s and transverse S waves that move at 4500 m/s. A seis
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Answer:

1234285.7 m or 1234.3 km

Explanation:

Let the distance be d, the time taken by P waves be t_P and the time taken by the S waves be t_S.

\text{Velocity}\dfrac{\text{Distance}}{\text{Time}}

\text{Time}\dfrac{\text{Distance}}{\text{Velocity}}

For the P waves,

t_P=\dfrac{d}{8000}

d=8000t_P

For the S waves,

t_S=\dfrac{d}{4500}

d=4500t_S

Equating the d,

8000t_P=4500t_S

Divide both sides of the equation by 500 to reduce the terms.

16t_P=9t_S

Since S waves arrive 2 minutes (= 120 seconds) after P waves,

t_S-t_P=120

t_S=120+t_P

Substitute this in the equation of the distance.

16t_P=9(t_P+120)

16t_P=9t_P+1080

7t_P=1080

t_P=\dfrac{1080}{7}

Substitute this in the equation for d involving t_P.

d=8000t_P

d=8000\times\dfrac{1080}{7}

d=1234285.7 \text{ m }= 1234.3 \text{ km}

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