Question

a baseball player standing on first base runs to second base and then third on one play. the total time it takes to run these two bases is 20 seconds. calculate the speed of the baseball player in feet per second. the first, second, and third bases are shown as white squares on the diagram
a 0 feet per second
b 18 feet per second
c 60 feet per second
d 90 feet per second

Explanation:

1. Recall the formula for speed:

• The formula for speed \(v\) is \(v=\frac{d}{t}\), where \(d\) is the distance traveled and \(t\) is the time taken.
• In a baseball - diamond, the distance between consecutive bases is 90 feet. The player runs from first base to second base and then from second base to third base. So the total distance \(d = 90+90=180\) feet.
• The time taken \(t = 20\) seconds.

1. Calculate the speed:

• Substitute \(d = 180\) feet and \(t = 20\) seconds into the speed formula \(v=\frac{d}{t}\).
• \(v=\frac{180}{20}=9\) feet per second.
• However, it seems there is a mistake in the options provided as 9 feet per second is not among them. Assuming we consider the distance from first - base to third - base directly (a straight - line distance across the diamond's diagonal which is not the normal running path but if we assume a wrong interpretation of the problem setup), using the Pythagorean theorem for a right - triangle with sides \(a = 90\) and \(b = 90\), the distance \(d=\sqrt{90^{2}+90^{2}}=\sqrt{2\times90^{2}} = 90\sqrt{2}\approx127.3\) feet. But this is not relevant as per normal baseball running. If we assume the intended distance is the sum of the two side - lengths of the square formed by the bases, \(d = 180\) feet.
• If we assume the problem is asking for the average speed over the two - base run and we use the sum of the side - lengths of the square of the bases, and calculate speed as \(v=\frac{180}{20}=9\). Since the options are wrong, if we assume the closest value based on wrong calculations or mis - understanding of the problem, we note that if we consider the distance from first to third as 180 feet (sum of two sides of the square of bases), the speed is 9 feet per second. But if we assume some error in the problem and we consider the distance from first to third as 180 feet and calculate speed:
• \(v=\frac{180}{20}=9\). Among the given options, if we assume a wrong approach and consider the distance as 180 feet, the closest value to our non - existent correct answer is:

Step1: Determine distance

The player runs two 90 - foot segments, so \(d = 90\times2=180\) feet.

Step2: Calculate speed

Using \(v=\frac{d}{t}\), with \(d = 180\) feet and \(t = 20\) seconds, \(v=\frac{180}{20}=9\) feet per second. Since 9 is not in the options, if we assume some mis - calculation in the problem setup and we consider the closest value conceptually, we note that the closest value to our calculated speed among the options is not present. But if we had to choose, we assume the intended distance was 180 feet and the closest option to the correct value (9 feet per second) is B.

Answer:

B. 18 feet per second (closest option to the correct value considering the problem setup and calculations)