Question

A sled is moving at a constant speed down a surface inclined at 45.0 with the horizontal and travels 30 meters in 4 seconds calculate the vertical velocity of the sled at the end of the 4 seconds

Answer 1

Because the speed of the sled is constant throughout this ordeal, we know that the instantaneous and average velocities are equal, and the velocity of the sled is

$v=\dfrac{-30\,\mathrm m}{4\,\mathrm s}=-7.5\,\dfrac{\mathrm m}{\mathrm s}$

(negative because we're taking the downward direction to be negative)

The vertical component of this vector is given by

$v_y=\|v\|\sin\theta$

where $\theta$ is the angle made by the velocity vector with the positive $x$-axis (taken to be the right direction). Here, $\theta=225^\circ$, so

$v_y=\left(7.5\,\dfrac{\mathrm m}{\mathrm s}\right)\sin225^\circ\approx-5.3\,\dfrac{\mathrm m}{\mathrm s}$