Question

Santa loses his footing and slides down a frictionless, snowy roof that is tilted at an angle of 30°. If Santa slides 10 m before reaching the edge, what is his speed as he leaves the roof?

Short answer

The velocity of Santa before he leaves the roof is 10 m/sec

Step-by-step solution

Step 1. Write the given information.

The Distance Santa slides before reaching edge is 10m

The angle of inclination is given as 30^o
Let the initial velocity of Santa is u. The time taken by Santa to reach the edge is t. The acceleration due to gravity is $g=10m/s^2$
The acceleration experienced by Santa is
$$\begin{gathered} a=g\sin (30°) \\ a=10(0.5) \\ a=5m/s^2 \end{gathered}$$

Step 2. To determine the velocity of Santa before he reaches edge

Let the velocity of Santa is$v$

The distance traveled is$S$
Using the equation of motion,

$S=ut+\frac{1}{2}a{t}^2$
Insert the known values in the above expression
$$\begin{gathered} 10=0t+\frac{1}{2}\left(5\right)t^2 \\ 10=2.5t^2 \\ {t}^2=\frac{10}{2.5}=4 \\ t=2sec \end{gathered}$$
Thus, the time taken by Santa to reach the edge is 2 sec.

Now, write the expression to determine the velocity of Santa
$$\begin{gathered} v=0+5\left(2\right) \\ v=10m/sec \end{gathered}$$

Therefore, the velocity of Santa is 10 m/sec