Question

Alberto is snowboarding down a mountain with a constant slope. the slope he is on has an overall length of 1560 feet. the top of the slope has a height of 4600 feet, and the slope of a vertical drop of 600 feet. It takes him 24 seconds to reach the bottom of the slope.
if we assume that Alberto's speed down the slope is consistent, what is his height above the bottom of the slope at 10 seconds into the Run?

Alberto says that he must have been going 50 miles per hour down the slope. do you agree? why or why not?

Answer 1

The slope of the equation is calculated as:

 $\frac{h_2-h_1}{t_2-t_1}=m$

Where $h_2$ is the height of the upper part of the slope and $h_1$ is the height of the low er part.

 $m=\frac{4000-4600}{24-0}$

$m=-25$

So, the equation of the line is:

$h-4600=-25(t-0)$

$h=-25t+4600$

With this equation we can find the height of Alberto after having passed 10 sec.

$h(10)=-25 (10)+4600\\h(10)=-250+4600\\h(10)=4350$

 After 10 seconds Alberto is 350 feet from the bottom of the slope.

Alberto's speed is:

$v=\frac{1560ft}{24s}=65ft/s$

The speed in miles per hour is:

$v=65ft /s*\frac{1 mile}{5280 ft}*\frac{3600s}{1 hour}\\v=44.32 miles/h$