Question

A 5.0 kg wooden sled is launched up a 25 ∘ snow-covered slope (μk = 0.06) with an initial speed of 9.0 m/s. What vertical height does the sled reach above its starting point?

Answer 1

The wooden sled reaches a vertical height of 4.16 meters above its starting point.

Step-by-step explanation:

To find the vertical height the sled reaches above its starting point, we can use the principle of conservation of mechanical energy. Initially, the sled has both kinetic energy and potential energy, but at the highest point, all of the kinetic energy is converted into potential energy. We can use the equations for kinetic energy and gravitational potential energy to find the height.

The initial kinetic energy of the sled is given by 1/2mv^2, which is (1/2)(5.0 kg)(9.0 m/s)^2 = 202.5 J. At the highest point, all of this kinetic energy will be converted into potential energy, given by mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Rearranging the equation, we have h = KE / (mg) = 202.5 J / (5.0 kg)(9.8 m/s^2) = 4.16 m. Therefore, the sled reaches a vertical height of 4.16 meters above its starting point.

Answer 2

The vertical height that the sled reached above its starting point is 3.6m.

How to find the vertical height?

Given:

Mass
`(\(m\))`: 5 kg

Angle
`(\(\theta\))`: 25°

Initial velocity
`(\(u\))`: 9 m/s

Coefficient of kinetic friction
`(\(\mu_k\))`: 0.06

Using Newton's second law:

`\[a = -g\sin\theta - \mu_k g\cos\theta\]`

`\[a = 9.81 * \sin(25^\circ) - 0.06 * 9.81 * \cos(25^\circ)\]`

`\[a \approx -4.67 \, \text{m/s}^2 \,`

Then, using the equation of motion to find displacement
`(\(S\))`at the maximum height
`(\(V = 0 \, \text{m/s}\))`:

`\[V^2 = u^2 + 2as\]`

`\[0^2 = 9^2 + 2 * (-4.67) * S\]`

`\[S \approx 8.617 \, \text{m} \,`

Now, to find the vertical height reached by the block above its starting point:

`\[h = S \sin\theta\]`

`\[h = 8.617 * \sin(25^\circ)\]`

`\[h \approx 3.6 \, \text{m} \,`

Therefore, the vertical height that the sled reached above its starting point is 3.6m