Question

1. -/1 points a child and sled with a combined mass of 41.0 kg slide down a frictionless slope. if the sled starts from rest and has a speed of 2.70 m/s at the bottom, what is the height of the hill? m resources read it

Explanation:

Step1: Apply conservation of mechanical energy

The initial mechanical energy $E_1$ is only potential energy $E_{p1}=mgh$ (since starts from rest, $v = 0$ so $K_1 = 0$), and the final mechanical energy $E_2$ is only kinetic energy $E_{k2}=\frac{1}{2}mv^{2}$ (at the bottom, $h = 0$ so $E_{p2}=0$). According to the conservation of mechanical energy $E_1 = E_2$, so $mgh=\frac{1}{2}mv^{2}$.

Step2: Solve for the height $h$

We can cancel out the mass $m$ from both sides of the equation $mgh=\frac{1}{2}mv^{2}$, getting $gh=\frac{1}{2}v^{2}$. Then $h=\frac{v^{2}}{2g}$. Given $v = 2.70\ m/s$ and $g = 9.8\ m/s^{2}$, we substitute these values: $h=\frac{(2.70)^{2}}{2\times9.8}$.
$h=\frac{7.29}{19.6}\approx0.372\ m$

Answer:

$0.372$