______A middle school baseball field is a diamond with a distance of 30ft. betwe
ID: 2850055 • Letter: #
Question
______A middle school baseball field is a diamond with a distance of 30ft. between the bases. Little Jimmy is making a run from 2nd base to 3rd base and hoping to get to home plate to win the game. When Little Jimmy is 10 ft. away from 3rd base, the distance between him and 3rd base is changing at a rate of root 10 ft,/s. Find how fast the distance between him and home plate is changing. ______Suppose that a particular Facebook post goes viral, and the amount of likes it receives grows at a rate proportional to the number of likes it currently has. Initially the Facebook post has 1000 likes. After 2 hours it has 100,000 likes. Find the time for the Facebook post to reach 1,000,000 likes. (Express your answer without any logarithms)Explanation / Answer
1. Answer
Let point B be II base, point A be III base, and C be home base. Let AC represent the x-axis, and BA represent the y-axis in the diagram below:
The boy is running to III base, so he is on line BA. His y-coordinate is changing at a rate of -(10 )ft/s, so we can say:
dy/dt=10 ft/s
His x-coordinate is staying constant at 30 ft.
We want to figure out how the rate at which his distance from point C is changing.
So, let's take the Pythagorean Theorem and differentiate it:
x^2+y^2= h^2 (h represents the hypotenuse)
2xdx/dt+2ydy/dt=2hdh/dt
implies xdx/dt+ydy/dt=hdh/dt
(We're looking for dh/dt because the hypotenuse is equivalent to the boy's distance from C.)
Solve for dh/dt
dh/dt=(xdx/dt+ydy/d)t/h
Remember though that his x-coordinate is always the same, so:
dx/dt=0
and this simplifies to:
dh/dt=y(dy/dt)/h
All we have to do is find the length of the hypotenuse when the boy is 10 ft away base III. Just use the Pythagorean Theorem!
a^2+b^2= c^2
10ft^2+30ft^2
c^2=10ft^2+30ft^2
c=10(10 )
Plugging in:
dh/dt=(10 )ft/s10ft/10(10 )ft = 1ft/s
2.Answer
here
dx/dt = (99000/2)
Using this,
(99000/2)=(999000/t)
implies
t= (999*2)/99
t= 20.1818182 (approx)hrs
Thus 1000,000 likes will be received after 20.1818182 (approx)hrs.
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