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The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of ${\displaystyle {45}^{\circ }}$. With what speed must the animal leave the ground to reach that height?

The wave function for a traveling wave on a taut string is (in SI units)(a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.100 m? What are (c) the wavelength and (d) the frequency of the wave? (e) What is the maximum transverse speed of an element of the string? ${\displaystyle y(x,t)=\left(0.350m\right)\sin (10\pi -3\pi x+\frac{\pi }{4})}$

A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by ${\displaystyle x\left(t\right)=b{t}^2-c{t}^3}$ , where ${\displaystyle b=2.40\frac{m}{s^2}}$ and ${\displaystyle c=0.120\frac{m}{s^3}}$ (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) Calculate the instantaneous velocity of the car at t=0, t = 5.0 s, and t = 10.0 s. (c) How long after starting from rest is the car again at rest?

A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. 
(a) The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 13 feet of rope out. What happens to the speed of the boat as it gets closer to the dock? 
(b) Suppose the boat is moving at a cons tant rate of 4 feet per second. Determine the speed at which the winch pulls in rope when the re is a tota l of 13 feet of rope out. What happens to the speed at which the winc h pulls in rope as the boat gets closer to the dock ?

a. When the displacement of a mass on a spring is ${\displaystyle \frac{1}{2}}$ A, what fraction of the mechanical energy is kinetic energy and what fraction is potential energy? b. At what displacement, as a fraction of A, is the energy half kinetic and half potential?

3.19 Win the Prize. In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (a) What is the height of the shelf above the point where the quar ter leaves your hand? (b) What is the vertical component of the velocity of the quarter just before it lands in the dish?

Point charges ${\displaystyle q1=50\mu C}$ and ${\displaystyle q2=-25\mu C}$ are placed 1.0 m apart. What is the force on a third charge ${\displaystyle q3=20\mu C}$ placed midway between q1 and q2?

A 2.0-kg projectile is fired with initial velocity components ${\displaystyle v_{0x}=30}$ m/s and ${\displaystyle v_{0y}=40}$ m/s from a point on the earth's surface. Neglect any effects due to air resistance. What is the kinetic energy of the projectile when it reaches the highest point in its trajectory? How much work was done in firing the projectile?

A helicopter carrying dr. evil takes off with a constant upward acceleration of ${\displaystyle 5.0\frac{m}{s^2}}$. Secret agent austin powers jumps on just as the helicopter lifts off the ground. Afterthe two men struggle for 10.0 s, powers shuts off the engineand steps out of the helicopter. Assume that the helicopter is infree fall after its engine is shut off and ignore effects of airresistance. 
a) What is the max height above ground reached by the helicopter? 
b) Powers deploys a jet pack strapped on his back 7.0s after leaving the helicopter, and then he has a constant downward acceleration with magnitude 2.0 m/s2. how far is powers above the ground when the helicopter crashes into the ground.

A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant but starts at .100 at P and increases linerly with distance past P, reaching a value of .600 at 12.5 m past point P. (a) Use the work energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1?

A floating ice block is pushed through a displacement d=(15m)i-(12m)j along a straight embankment by rushing water, which exerts a force F=(210N)i-(150N)j on the block. How much work does theforce do on the block during the displacement?

Find the tension in each cord in Figure if the weight ofthe suspended object is w. 
a)  
b)

Four point charges form a square with sides of length d, as shown in the figure. In the questions that follow, use the constant k in place of ${\displaystyle \frac{1}{4\pi {ϵ}_0}}$.

Part A
What is the electric potential ${\displaystyle V_{\to t}}$ at the center of the square?
Make the usual assumption that the potential tends to zero far away from a charge.
Express your answer in terms of q ,d, and appropriate constants.
${\displaystyle V_{\to t}=}$ 
Part B
What is the contribution ${\displaystyle U_{2q}}$ to the electric potential energy of the system, due to interactions involving the charge 2q ?
Express your answer in terms of q, d, and appropriate constants.
${\displaystyle U_{2q}=}$
Part C
What is the total electric potential energy ${\displaystyle U_{\to t}}$ of this system of charges? Express your answer in terms of q, d, and appropriate constants.
${\displaystyle U_{\to t}=}$
, plz i want just the final answers , thanks

The initial velocity of a car, vi, is 45 km/h in the positivex direction. The final velocity of the car, vf, is 66 km/h indirection that points 75 degrees above the positive x axis. 
a) sketch the vectors -vi, vf and change in v. (b) findthe magnitude and direction in change of velocity. 
For b..my answer was -37.93 km/h and -88.41 degrees for direction.

From her bedroom window a girl drops a water-filled balloon to the ground 6.0 m below. If the balloon is released from rest,how long is it in the air?

You are on the roof of the physics building, 46.0 m above the ground. Your physics professor, who is 1.80 tall, is walking along side the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your professor's head, how far from the building should the professor be when you release the egg? Assume that the egg is in free fall.Take the free fall acceleration to be ${\displaystyle 9.80\frac{m}{s^2}}$

A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60 m high. At the bottom, it strikes a block of mass=7.00 kg which is at rest on a horizontal surface in the picture. If the collision is elastic, and friction can be ignored, determine (a)the speeds of the two blocks after the collision, and (b) how far back up the incline the smaller mass will go.

Two point charges ${\displaystyle q_1=+2.40}$ nC and ${\displaystyle q_2=-6.50}$ nC are 0.100 m apart. Point A is midway between them and point B is 0.080 m from ${\displaystyle q1}$ and 0.060 m from ${\displaystyle q_2}$. Take the electric potential to be zero at infinity.

(a) Find the potential at point A.
(b) Find the potential at point B.
(c) Find the work done by the electric field on a charge of 2.50 nC that travels from point B to point A.

An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of ${\displaystyle 6.64\cdot {10}^{-27}}$ kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.10 T magnetic field. 
A) What is the diameter of the path followed by this alpha particle? 
B) What effect does the magnetic field have on the speed of the particle? 
C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field? 
D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?

A model airplane of mass 0.750 kg flies in a horizontal circle at the end of a 60.0 m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0° with the horizontal. The forces exerted on the airplane are the pull of the control wire, the gravitational force, and aerodynamic lift, which acts at 20.0° inward from the vertical.