Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Solution :
From the triangle,
[tex]$x^2 = s^2 + 90^2$[/tex]
[tex]$x = \sqrt{s^2 + 90^2}$[/tex]
Now differentiating w.r.t "t", we get
[tex]$\frac{dx}{dt}=\frac{d}{dt}\left(s^2 +90^2 \right)^{1/2}$[/tex]
[tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{\frac{1}{2}-1} \cdot 2s \cdot \frac{ds}{dt}$[/tex] [chain rule]
[tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{-\frac{1}{2}} \cdot 2s \cdot \frac{ds}{dt}$[/tex]
[tex]$=\frac{s}{\left(s^2 + 90^2\right)^{\frac{1}{2}}} . \frac{ds}{dt}$[/tex]
But given that [tex]$\frac{ds}{dt}$[/tex] = 100 ft/s
When all the ball crosses the third base, this means that s = 90. So substituting the value of s and [tex]$\frac{ds}{dt}$[/tex] in [tex]$\frac{dx}{dt}$[/tex] , we get
[tex]$\frac{dx}{dt} = \frac{90}{\left(90^2 +90^2\right)^{1/2}} \times 100$[/tex]
[tex]$\frac{dx}{dt} = \frac{90}{\sqrt{8100+8100}} \times 100$[/tex]
[tex]$\frac{dx}{dt} = 50\sqrt2$[/tex]
= 70.710 ft/s
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
