At t = 0 a batter hits a baseball with an initial speed of 32 m/s at a 55° angle to the

Chapter 3, Problem 73GP

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QUESTION:

At t = 0 a batter hits a baseball with an initial speed of 32 m/s at a \(55^{\circ}\) angle to the horizontal. An outfielder is 85 m from the batter at t = 0, and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of \(22^{\circ}\) with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder’s line of sight to home plate.

         

                                                   Figure 3-50

Equation Transcription:

Text Transcription:

55 degrees

22 degrees

Questions & Answers

QUESTION:

At t = 0 a batter hits a baseball with an initial speed of 32 m/s at a \(55^{\circ}\) angle to the horizontal. An outfielder is 85 m from the batter at t = 0, and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of \(22^{\circ}\) with the plane in which the ball moves (see Fig. 3-50). What speed and direction must the fielder take in order to catch the ball at the same height from which it was struck? Give angle with respect to the outfielder’s line of sight to home plate.

         

                                                   Figure 3-50

Equation Transcription:

Text Transcription:

55 degrees

22 degrees

ANSWER:

Step 1 of 7

To solve this problem, we need to analyze the motion of the baseball and determine the velocity and direction the outfielder needs to take in order to catch the ball at the same height from which it was struck.

Let's break down the problem into components and establish a coordinate system. We'll use the x-axis as the direction from home plate to the outfielder and the y-axis as the vertical direction.

The first part requires you to find the distance the baseball travels. The second part requires you to find the distance and velocity the outfielder has to run.

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