A skydiver parachutes to the ground. The height y (in feet) of the skydiver after x seconds is #y=-10x+3000#, how do you graph and Interpret the x-intercept and the slope?

1 Answer
Nov 12, 2016

Answer:

See description

Explanation:

You have to try and understand what the numbers are doing and associate that with actual events.

It is stated that #y# is height 'above ground' . If he goes 'below ground than he is in trouble!

The right hand side (RHS) has negative #10x# which reduces 3000 in relation to time #x#. Consequently 3000 feet must be the initial height. it is also the y-intercept.

The #-10x# has to be the count of feet as the parachutist descends in #x# seconds. It is also the slope (gradient) of the graph.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
At the point where the graph crosses the x-axis it means that #y=0# and #y# is the height above ground.

Consequently the x-intercept is at the point of reaching the ground.

The slope is the rate of descent which is constant as time (x) increases.
..................................................................................................................
Actually the rate of descent is a very rounded value. To 2 decimal places I think it is 9.81 metres per second per second in metric form.

In imperial form it is something like 32.2 feet per second per second.
....................................................................................................................

#color(blue)("To determine the time to reach ground level.")#

Set #y=0# giving

#0=-10x+3000#

#=>+10x=3000#

#color(blue)(x=3000/10 = 300" seconds" -> 5" minutes exactly")#

Tony B