# What is the speed of the object after it has slid up the hill?

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✅Question :

What is the speed of the object after it has slid up the hill? The hill height is 1.6 m (round this answer to two significant figures).

To calculate the speed of the object after it has slid up the hill, we can use the principle of conservation of mechanical energy. The initial potential energy when the object is at the bottom of the hill is converted into kinetic energy as it moves up the hill.

The potential energy (PE) at the bottom of the hill is given by: PE_initial = m * g * h_initial

where: m = mass of the object g = acceleration due to gravity h_initial = height of the hill (1.6 m)

As the object moves up the hill, its potential energy is converted into kinetic energy, and at the top of the hill, all the initial potential energy is transformed into kinetic energy:

KE_final = PE_initial

The kinetic energy (KE) is given by the formula: KE = 0.5 * m * v^2

where: v = final velocity of the object

Setting the initial potential energy equal to the final kinetic energy: 0.5 * m * v^2 = m * g * h_initial

Solving for v: v^2 = 2 * g * h_initial

Taking the square root and plugging in the given values: v = √(2 * 9.8 m/s² * 1.6 m) v ≈ 6.29 m/s

Rounded to two significant figures, the speed of the object after it has slid up the hill is approximately 6.3 m/s.

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