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Answer :
Answer:
ball will fall down by y = 2.63 ft
Explanation:
As we know that fastest pitch for major league is given as
[tex]v = 100.8 mph[/tex]
here we know that
[tex]1 mph = 1.467 ft/s[/tex]
now we have
[tex]v = 100.8 mph = 100.8 \times 1.467 ft/s[/tex]
[tex]v = 147.87 ft/s[/tex]
now the distance of home plate is given as
[tex]d = 60 ft[/tex]
so here the time taken by the ball top reach home plate is given as
[tex]t = \frac{d}{v}[/tex]
[tex]t = \frac{60}{147.87}[/tex]
[tex]t = 0.406 s[/tex]
Now the displacement of ball in vertical direction is given as
[tex]y = \frac{1}{2}gt^2[/tex]
[tex]y = \frac{1}{2}(32)(0.406)[/tex]
[tex]y = 2.63 ft[/tex]
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Rewritten by : Barada
The ball would fall vertically by approximately 2.10 feet by the time it reaches home plate 60.0 feet away when thrown horizontally at 100.8 mi/hr.
How to find how far would the ball fall vertically by the time it reached home plate 60.0 ft away
To find how far the ball would fall vertically by the time it reaches home plate, we can use the equations of motion. We'll first convert the velocity from miles per hour (mi/hr) to feet per second (ft/s) because the distance is given in feet.
First, convert the velocity:
1 mile = 5280 feet
1 hour = 3600 seconds
So, \(v\) in ft/s is:
[tex]\[ v = \frac{100.8 \, \text{mi/hr} \times 5280 \, \text{ft/mi}}{3600 \, \text{s/hr}} \approx 147.2 \, \text{ft/s} \][/tex]
Now, we can use the following kinematic equation to find the vertical distance (\(y\)) the ball falls:
[tex]\[ y = \frac{1}{2}gt^2 \][/tex]
We need to find \(t\), which we can calculate using the horizontal distance (\(d\)) and the horizontal velocity (\(v\)):
[tex]\[ t = \frac{d}{v} = \frac{60.0 \, \text{ft}}{147.2 \, \text{ft/s}} \approx 0.407 \, \text{s} \][/tex]
Now, substitute \(t\) into the vertical motion equation:
[tex]\[ y = \frac{1}{2} \cdot 32.2 \, \text{ft/s}^2 \cdot (0.407 \, \text{s})^2 \][/tex]
Calculate \(y\):
[tex]\[ y \approx 2.10 \, \text{ft} \][/tex]
So, the ball would fall vertically by approximately 2.10 feet by the time it reaches home plate 60.0 feet away when thrown horizontally at 100.8 mi/hr.
Learn more about velocity at https://brainly.com/question/80295
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