Physics Questions & Answers

14. A diver is on a hill overlooking a lake. If the hill is 45 feet above the surface of the water and the liver jumps horizontally \( \left(\theta=0^{\circ}\right) \) with an initial speed of \( 20.0 \mathrm{ft} / \mathrm{sec} \), how far from the hill will the iver hit the lake?

2. De los siguientes movimientos observados durante un mismo intervalo de tiempo, ¿cuál tiene mayor aceleración y por qué? a. Un ciclista cuya rapidez pasa de \( 25 \mathrm{~m} / \mathrm{s} \) a \( 45 \mathrm{~m} / \mathrm{s} \). b. Un automóvil que parte del reposo y alcanza una velocidad de \( 72 \mathrm{~km} / \mathrm{h} \).

Un cuerpo inicia su movimiento para \( t=0 \mathrm{~s} \) en la posición \( x=5 \mathrm{~cm} \), luego alcanza la posición \( x=23 \mathrm{~cm} \) y finalmente se devuelve a la posición \( x \) \( =17 \mathrm{~cm} \). Si emplea 15 s en todo el recorrido, ¿cuál es su velocidad media?

5- [similar to Byron-Fuller 2.9] Consider the action \( I\left[\psi_{r}, \psi_{i}\right]=\int \mathcal{L} d t d x d y d z \) where \[ \mathcal{L}=\frac{\hbar^{2}}{2 m} \nabla \psi^{*} \cdot \nabla \psi+V \psi^{*} \psi-\frac{i \hbar}{2}\left(\dot{\psi} \psi^{*}-\psi \dot{\psi}^{*}\right) \] is called Lagrangian density and \( \psi=\psi_{r}+i \psi_{i}(\hbar \) and \( m \) are constants, \( V \) is a given function of \( x, y \), and \( z \), star denotes complex conjugation, and dot means \( d / \partial t) \). Show that the Euler-Lagrange equations for this action lead to the Schrödinger equation: \[ \left(-\frac{\hbar^{2}}{2 m} \nabla^{2}+V\right) \psi=i \hbar \frac{\partial \psi}{\partial t} \]

(c) While falling, \( 80 \% \) of the 0.537 J converted to other types of energy is absorbed by the ball, The specific heat capacity of the ball is \( 8200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{C}^{-1} \). Calculate the rise in temperature of the ball as it falls.

Cuando un hombre de 60 Kg se introduce en un auto, el CG del vehículo desciende \( 0,8 \mathrm{~cm} \) Si la masa del auto es de 500 Kg ¿Cuál será el periodo de oscilación? a) Cuando el auto está cargado. b) Cuando el auto está vacio

\begin{tabular}{l} Exercise Ch.3\#3: Gotta Go! \\ \hline On your way to the restroom! \\ Thankfully, there is no video now, but there are strobe snapshots. The restroom is to the \\ LEFT and way down the long hall. We analyze "snapshots" your "friend" took, because \\ kinematics is our thing. This time we have six "strobe" pictures taken every \( 2 \mathrm{~s}: t_{1}=0 \mathrm{~s} \) \\ (started video), \( t_{2}=2.00 \mathrm{~s}, t_{3}=4.00 \mathrm{~s} \), and so on, up to \( t_{6} \). Again, let's call the position at \( t_{1}= \) \\ 0 s the origin and write \( x_{1}=0 \mathrm{~m} \) and take the direction you walk \( / \) run to be + . Our snapshots \\ show that \( x_{2}=2.0 \mathrm{~m}, x_{3}=5.0 \mathrm{~m}, x_{4}=9.0 \mathrm{~m}, x_{5}=11.5 \mathrm{~m}, x_{6}=12.5 \mathrm{~m} \). \\ a. Sketch the process and label everything you can about each state. Show the choice for \\ the + direction with an axis arrow labeled " \( +x \) " \end{tabular}

The two forces \( \stackrel{\rightharpoonup}{F_{1}}=3 \hat{i}-\hat{j}, \stackrel{\rightharpoonup}{F_{2}}=-9 \hat{i}+3 \hat{j} \) act at the two points \( A(-1,0), B(1,2) \) respectively, then the point of intersection of the line of action of the resultant of the twe forces with \( \overleftrightarrow{A B} \) \( \begin{array}{llll}\text { (a) }(2,3) & \text { (b) }(-6,2) & \text { (c) }(3,1) & \text { (d) }(2,5)\end{array} \)

5 In una corsa un atleta accelera in modo uniforme e rag- giunge la velocità di \( 1,4 \mathrm{~m} / \mathrm{s} \) in 12 s . a) Qual è l'accelerazione dell'atleta? b) Che velocità raggiunge in 15 secondi? c) Quanto spazio percorre in 15 secondi?

4 Un'automobile, che si muove a velocità costante di \( 76 \mathrm{~km} / \mathrm{h} \), si trova a 120 m da un incrocio. a) In quanto tempo raggiunge l'incrocio? b) Scrivi e rappresenta graficamente la legge oraria.