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=(-30\,\mathrm m)/(4\,\mathrm s)=-7.5\,(\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\,(\mathrm m)/(\mathrm s)\right)\sin225^\circ\approx-5.3\,(\mathrm m)/(\mathrm s)`