A7.5 kg stone moves up frictionless hill that slopes upward at 41 above the horizontal. if the stone has a initial velocity of 8.5 m/s at the bottom, how far (as measured along the surface of the hill) will it go before stopping?

The stone will reach 3.2 m along the surface of the hill before stopping.

Explanation:

Let the height reached by the stone be 'h' m

Given:

Mass of the stone is 7.5 kg.

Angle of inclination is,

Initial velocity of the stone at the bottom is,

Final velocity of the stone at the top is 0 m/s.

Now, as per conservation of energy principle, sum of total energy is always conserved. Therefore, decrease in kinetic energy is equal to the increase in its potential energy.

Increase in Potential Energy = Decrease in Kinetic Energy

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Plug in the given values and solve for 'h'. This gives,

Now, slant height is given using the trigonometric ratio. The slant length 'L' is the hypotenuse and 'h' is the opposite side. Therefore,

Therefore, the stone will reach 3.2 m along the surface of the hill before stopping.

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