Question

The tennis team has a robot that picks up tennis balls. The tennis court is 36 feet wide and 78 feet long. The robot

Answer 1

Answer:

$t = t_1 +t_2 = 4 sec+6 sec = 10 sec$

Step-by-step explanation:

Let's call the initial point $I= (x_i=8,y_i=10)$ and the second point $R=(x_r = 16, 20)$ we can find the distance between these two points with the following formula:

$d_1 = \sqrt{(x_r -x_i)^2 +(y_r -y_i)^2}$

And if we replace we got:

$d_1 = \sqrt{(16 -8)^2 +(20 -10)^2} =2\sqrt{41}$

So since we know the time in order to reach the point R we can find the velocity like this:

$v=\frac{d_1}{t_1} = \frac{2\sqrt{41}}{4}=\frac{\sqrt{41}}{2}$

And this velocity is constant along all the displacement.

Let's call the final point $F =(x_f = 28, y_f = 35)$

And we can find the distance between the point R and F $d_2$ like this:

$d_2 = \sqrt{(x_f -x_r)^2 +(y_f -y_r)^2}$

And if we replace we got:

$d_2 = \sqrt{(28 -16)^2 +(35 -20)^2}=3\sqrt{41}$

Since the velocity is constant we can find the time between point R and F like this:

$t_2 = \frac{3\sqrt{41}}{\frac{\sqrt{41}}{2}}=6 sec$

And we are interested on "When will it  pick up the ball located at position (28,35)?" And then the total time would be:

$t = t_1 +t_2 = 4 sec+6 sec = 10 sec$

The figure attached illustrate the problem.