# Problem 3.62, Young and Freedman-On the Flying Trapeze

• james brug
In summary, the Texas Tumblers circus act involves Mary Belle launching herself from a trapeze at an angle of 53 degrees and being caught by Joe Bob, who is positioned 6.1m above and 8.2m horizontally from her launch point. To reach Joe Bob, Mary Belle must have an initial speed of 13.7m/s, with a y-velocity of 10.93m/s and an x-velocity of 8.24m/s. However, according to Mastering Physics, these values should be 14m/s, 11.2m/s, and 8.4m/s. At the top of her parabolic trajectory, Mary Belle's y-velocity is
james brug
Problem 3.62, Young and Freedman--On the Flying Trapeze

A new circus act is called the Texas Tumblers. Mary Belle swings from a trapeze, projects herself at an angle of 53 degrees, and is supposed to be caught by Joe Bob whose hands are 6.1m above and 8.2 horizontally from her launch point. You can ignore air resistance.

(a) What initial speed $$V_o$$, must Mary Belle have just to reach Joe Bob?

(b) For the initial speed calculated in part a, what are the magnitudes and direction of her velocity when Mary reaches Joe?

My attempt at a solution

(a) $$V_y^2=V_{0y}^2+2a_y(y-y_0)$$

$$-V_{0y}^2=-19.6m/s^2(6.1m)$$ set $$V_y$$ equal to 0

$$V_{0y}=10.93m/s$$ initial y velocity

$$tan(53^{\circ}) =\frac{10.93}{x} \rightarrow x= 8.24 m/s$$ x velocity

magnitude=13.7 m/s

Mastering Physics says these values should be 14m/s,11.2 m/s, and 8.4m/s.

(b) The magnitude according to Mastering Physics is 8.4m/s, which is also her x-velocity component, $$V_x$$. This means that Mary Joe is at the top of her parabolic trajectory, where her y-velocity, $$V_y$$ is 0, right?.

Well, I got the same values as you did, and to your (b), yes. I guess the textbook just got it wrong.

Yes, according to the given information, Mary Belle is at the top of her parabolic trajectory when her y-velocity is 0. However, it is important to note that this is assuming no air resistance. In reality, air resistance would affect the trajectory and velocity of Mary Belle at this point.

## 1. What is the problem being discussed in Young and Freedman's "On the Flying Trapeze"?

The problem being discussed is the motion of a flying trapeze artist as they swing back and forth between two platforms, with one platform being higher than the other.

## 2. What are the key concepts involved in solving this problem?

The key concepts involved are conservation of energy, conservation of angular momentum, and the principles of circular motion.

## 3. How is the problem typically presented in physics textbooks?

The problem is typically presented as a diagram with a trapeze artist swinging back and forth between two platforms, along with the relevant measurements and variables involved.

## 4. What are some common approaches to solving this problem?

Some common approaches include using the equations for conservation of energy and angular momentum, setting up a free-body diagram, and breaking down the motion into components.

## 5. How does solving this problem relate to real-world situations?

Solving this problem can help us understand the mechanics behind the motion of a trapeze artist, and can also be applied to other situations involving circular motion and conservation laws, such as the orbit of a satellite or the motion of a pendulum.

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