QuestionJames throws a 90 mph fastball. If it takes 1.8 seconds to reach home plate, find the distance to the mound in meters.

Studdy Solution

STEP 1

Assumptions1. The speed of the baseball is90 miles/hour. The time it takes for the ball to reach home plate is1.8 seconds3. We need to find the distance in meters

STEP 2

First, we need to convert the speed from miles per hour to meters per second. We know that1 mile is approximately1609.34 meters, and1 hour is3600 seconds.
$Speed\, in\, m/s = Speed\, in\, miles/hour \\times \frac{1609.34\, m/mile}{3600\, s/hour}$

STEP 3

Now, plug in the given value for the speed in miles per hour to calculate the speed in meters per second.
$Speed\, in\, m/s =90\, miles/hour \\times \frac{1609.34\, m/mile}{3600\, s/hour}$

STEP 4

Calculate the speed in meters per second.
$Speed\, in\, m/s =90\, miles/hour \\times \frac{1609.34\, m/mile}{3600\, s/hour} =40.2336\, m/s$

STEP 5

Now that we have the speed in meters per second, we can find the distance the ball travels. We can do this by multiplying the speed by the time it takes for the ball to reach home plate.
$Distance = Speed\, in\, m/s \\times Time\, in\, seconds$

STEP 6

Plug in the values for the speed in meters per second and the time in seconds to calculate the distance.
$Distance =40.2336\, m/s \\times1.8\, seconds$

STEP 7

Calculate the distance.
$Distance =40.2336\, m/s \\times1.\, seconds =72.4205\, meters$ The pitching mound is approximately72.4205 meters from home plate.

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