/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 A ball thrown by a pitcher on a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 14

A ball thrown by a pitcher on a women's softball team is timed at 65.0 mph. The distance from the pitching rubber to home plate is \(43.0 \mathrm{ft}\). In major league baseball the corresponding distance is \(60.5 \mathrm{ft}\). If the batter in the softball game and the batter in the baseball game are to have equal times to react to the pitch, with what speed must the baseball be thrown? Assume the ball travels with a constant velocity. [Hint: There is no need to convert units; set up a ratio.]

Short Answer

Expert verified
Answer: The baseball must be thrown at approximately 93 mph for the batters in both games to have an equal reaction time.

Step by step solution

01

Write down the given information for the softball pitch

We are given: - Softball pitch speed: \(65.0 \mathrm{mph}\) - Softball pitch distance: \(43.0 \mathrm{ft}\)
02

Write down the given information for the baseball pitch

We are given: - Baseball pitch distance: \(60.5 \mathrm{ft}\) - Baseball pitch speed: Unknown (\(x\))
03

Use the velocity formula to find the time of the softball pitch

Since we have the speed and distance for the softball pitch, we can use the formula for the velocity \(v_s = \frac{d_s}{t_s}\), where \(v_s\) is the softball pitch speed, \(d_s\) is the softball pitch distance, and \(t_s\) is the softball pitch time. Rearrange the formula to solve for \(t_s\): \(t_s = \frac{d_s}{v_s}\)
04

Use the velocity formula to find the time of the baseball pitch

Since we have the distance for the baseball pitch and we want the reaction times to be equal, we can use the formula for the velocity \(v_b = \frac{d_b}{t_b}\), where \(v_b\) is the baseball pitch speed, \(d_b\) is the baseball pitch distance and \(t_b\) is the baseball pitch time. Since we want the reaction times to be equal, we know that \(t_s = t_b\). Thus, we can rewrite the velocity formula for the baseball pitch as: \(v_b = \frac{d_b}{t_s}\)
05

Set up a ratio using the velocity formulas

Now, we can set up a ratio using the softball and baseball pitch velocity formulas. \(\frac{d_s}{v_s} = \frac{d_b}{v_b}\)
06

Substitute the given values and solve for the baseball pitch speed

Substitute the given values into the equation and solve for \(v_b\): \(\frac{43.0 \mathrm{ft}}{65.0 \mathrm{mph}} = \frac{60.5 \mathrm{ft}}{v_b}\) Cross-multiply to obtain: \(43.0 \mathrm{ft} \times v_b = 65.0 \mathrm{mph} \times 60.5 \mathrm{ft}\) Now, divide by \(43.0 \mathrm{ft}\): \(v_b = \frac{65.0 \mathrm{mph} \times 60.5 \mathrm{ft}}{43.0 \mathrm{ft}}\) \(v_b \approx 93.023 \mathrm{mph}\) The baseball must be thrown at approximately 93 mph for the batters in both games to have an equal reaction time.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the problems, please assume the free-fall acceleration $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ unless a more precise value is given in the problem statement. Ignore air resistance. A rocket is launched from rest. After 8.0 min, it is \(160 \mathrm{km}\) above the Earth's surface and is moving at a speed of $7.6 \mathrm{km} / \mathrm{s} .$ Assuming the rocket moves up in a straight line, what are its (a) average velocity and (b) average acceleration?
A train is traveling south at \(24.0 \mathrm{m} / \mathrm{s}\) when the brakes are applied. It slows down with a constant acceleration to a speed of $6.00 \mathrm{m} / \mathrm{s}\( in a time of \)9.00 \mathrm{s} .$ (a) Draw a graph of \(v_{x}\) versus \(t\) for a 12 -s interval (starting \(2 \mathrm{s}\) before the brakes are applied and ending 1 s after the brakes are released). Let the \(x\) -axis point to the north. (b) What is the acceleration of the train during the \(9.00-\mathrm{s}\) interval? \((\mathrm{c})\) How far does the train travel during the $9.00 \mathrm{s} ?$
At 3 P.M. a car is located \(20 \mathrm{km}\) south of its starting point. One hour later it is \(96 \mathrm{km}\) farther south. After two more hours, it is \(12 \mathrm{km}\) south of the original starting point. (a) What is the displacement of the car between 3 P.M. and 6 P.M.? (b) What is the displacement of the car from the starting point to the location at 4 P.M.? (c) What is the displacement of the car between 4 P.M. and 6 P.M.?
A relay race is run along a straight-line track of length \(300.0 \mathrm{m}\) running south to north. The first runner starts at the south end of the track and passes the baton to a teammate at the north end of the track. The second runner races back to the start line and passes the baton to a third runner who races \(100.0 \mathrm{m}\) northward to the finish line. The magnitudes of the average velocities of the first, second, and third runners during their parts of the race are \(7.30 \mathrm{m} / \mathrm{s}, 7.20 \mathrm{m} / \mathrm{s}\) and \(7.80 \mathrm{m} / \mathrm{s},\) respectively. What is the average velocity of the baton for the entire race? [Hint: You will need to find the time spent by each runner in completing her portion of the race.]
The St. Charles streetcar in New Orleans starts from rest and has a constant acceleration of \(1.20 \mathrm{m} / \mathrm{s}^{2}\) for \(12.0 \mathrm{s} .\) (a) Draw a graph of \(v_{x}\) versus \(t .\) (b) How far has the train traveled at the end of the \(12.0 \mathrm{s} ?\) (c) What is the speed of the train at the end of the \(12.0 \mathrm{s} ?\) (d) Draw a motion diagram, showing the streetcar's position at \(2.0-\mathrm{s}\) intervals.
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Torque and Rotational Motion

Read Explanation

Dynamics

Read Explanation

Famous Physicists

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.