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Chapter 2: Problem 102

The sport with the fastest moving ball is jai alai, where measured speeds have reached \(303 \mathrm{~km} / \mathrm{h}\). If a professional jai alai player faces a ball at that speed and involuntarily blinks, he blacks out the scene for \(100 \mathrm{~ms}\). How far does the ball move during the blackout?

Short Answer

Expert verified
The ball moves approximately 8.417 meters during the blackout.

Step by step solution

01

Convert time from milliseconds to seconds

The time given is 100 milliseconds. To make calculations easier, we convert this time into seconds by dividing the milliseconds by 1000. Thus, \(100 \text{ ms} = \frac{100}{1000} \text{ s} = 0.1 \text{ s}\).
02

Convert speed from kilometers per hour to meters per second

The speed of the ball is given as 303 kilometers per hour. We convert this speed to meters per second using the conversion factor: \(1 \text{ km/h} = \frac{1000}{3600} \text{ m/s}\). Therefore, \(303 \text{ km/h} = 303 \times \frac{1000}{3600} \text{ m/s} \approx 84.17 \text{ m/s}\).
03

Calculate the distance traveled during the blink

The distance the ball travels during the blink can be calculated using the formula \(d = v \times t\), where \(v\) is the speed and \(t\) is the time. Using the converted values, we have \(d = 84.17 \text{ m/s} \times 0.1 \text{ s} = 8.417 \text{ m}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit Conversion
Unit conversion is essential in physics to ensure accuracy in calculations. Converting units involves transforming one set of measurements into another. This is crucial when dealing with quantities like speed or time that are provided in non-standard units for your calculations.
For instance, in the given problem, the time is initially provided as 100 milliseconds. Milliseconds are a less common unit in physics calculations, so it is more effective to convert it into seconds. This is done by dividing milliseconds by 1000, since 1 second equals 1000 milliseconds. Therefore, 100 milliseconds is the same as 0.1 seconds.
Similarly, speed was originally provided in kilometers per hour (km/h). Speed in meters per second (m/s) is more convenient when dealing with distances in kilometers or meters and times in seconds. The conversion from km/h to m/s is done using the conversion factor 1000/3600, since 1 kilometer equals 1000 meters, and 1 hour is 3600 seconds. Hence, converting 303 km/h to m/s results in approximately 84.17 m/s.
Kinematic Equations
Understanding kinematic equations is fundamental in solving problems related to motion. These equations relate to quantities like displacement, velocity, and time. Kinematic equations apply to objects moving with constant velocity or uniform acceleration.
In the problem of jai alai, the blink is a brief event during which the ball moves in a straight line at a constant velocity, thus simplifying the scenario to use a basic kinematic equation \(d = v \times t\), where:
  • d is the distance traveled.

  • v is the constant velocity of the ball.

  • t is the time duration the velocity is maintained.
Given the constant speed and short blink duration, the use of this straightforward equation makes it efficient to find the distance covered during the blink. Hence, the distance is calculated by multiplying the speed (84.17 m/s) with the time (0.1 s), deriving an answer of 8.417 meters.
Speed Calculation
Speed calculation is a key part of motion analysis in physics. Speed indicates how quickly an object moves from one place to another. It's measured as the distance covered over a given period. Calculating speed can involve converting measurements into compatible units to then analyze or solve problems.
In the described exercise, the speed calculation involves first converting the units of given speed, ensuring compatibility for further calculations. The speed is given as 303 km/h, which translates to roughly 84.17 m/s after conversion. This speed now provides a convenient means to calculate how far the jai alai ball travels while the player blinks.
By keeping consistent units across speed and time, the calculation using the basic kinematic equation is simplified. The final speed value, calculated in meters per second, ensures accuracy in determining the exact distance the ball travels within the blink, providing a clear insight into the efficiency of physics concepts.

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Most popular questions from this chapter

A rock is shot vertically upward from the edge of the top of a tall building. The rock reaches its maximum height above the top of the building \(1.60 \mathrm{~s}\) after being shot. Then, after barely missing the edge of the building as it falls downward, the rock strikes the ground \(6.00 \mathrm{~s}\) after it is launched. In SI units: (a) with what upward velocity is the rock shot, (b) what maximum height above the top of the building is reached by the rock, and (c) how tall is the building?

A red train traveling at \(72 \mathrm{~km} / \mathrm{h}\) and a green train traveling at \(144 \mathrm{~km} / \mathrm{h}\) are headed toward each other along a straight, level track. When they are \(950 \mathrm{~m}\) apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of \(1.0 \mathrm{~m} / \mathrm{s}^{2}\). Is there a collision? If so, answer yes and give the speed of the red train and the speed of the green train at impact, respectively. If not, answer no and give the separation between the trains when they stop.

A drowsy cat spots a flowerpot that sails first up and then down past an open window. The pot is in view for a total of \(0.50 \mathrm{~s}\), and the top-to- bottom height of the window is \(2.00 \mathrm{~m}\). How high above the window top does the flowerpot go?

A pilot flies horizontally at \(1300 \mathrm{~km} / \mathrm{h}\), at height \(h=35 \mathrm{~m}\) above initially level ground. However, at time \(t=0\), the pilot begins to fly over ground sloping upward at angle \(\theta=4.3^{\circ}\) (Fig. \(2-41\) ). If the pilot does not change the airplane's heading, at what time \(t\) does the plane strike the ground?

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of \(v_{0}=55 \mathrm{~km} / \mathrm{h} ;\) your best deceleration rate has the magnitude \(a=5.18 \mathrm{~m} / \mathrm{s}^{2}\). Your best reaction time to begin braking is \(T=0.75 \mathrm{~s}\). To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at \(55 \mathrm{~km} / \mathrm{h}\) if the distance to the intersection and the duration of the yellow light are (a) \(40 \mathrm{~m}\) and \(2.8 \mathrm{~s}\), and (b) \(32 \mathrm{~m}\) and \(1.8 \mathrm{~s}\) ? Give an answer of brake, continue, either (if either strategy works), or neither (if neither strategy works and the yellow duration is inappropriate).
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