Part I

An object is through from the origin at an initial velocity of v₀ and at an angle θ in relation to the horizon.

a. write out r^->(t) for the object

b. find the velocity vector and acceleration vector for the object.

c. calculate the angle between the velocity vector and the acceleration vector at any point in time t.

Part II

An object is moving upwards on a slope at initial velocity v₀. There is friction between the object and the slope.

a. Calculate the amount of time it will take for the body to return to its initial position.

b. what is the ratio between the final velocity and the initial velocity?

Thank you!

A baseball player is 98m away from home plate when he throws the ball at a 30° angle above horizontal from a height of 1.45 m (the height of his hand).

a. What is the initial speed of the throw for the ball to land exactly on home plate? In order to solve this problem, set up equations for x and y position vs time. Put in all known values. You will have two remaining unknowns: v0(the magnitude of the initial velocity) and t. Solve the system of equations.

b.How long does it take the ball to get to home plate?

c.What is the maximum height that the ball is above the ground?

d. Sketch with coordinate system

Radioactive isotopes often occur together in mixtures. Suppose a 220g sample contains ¹³¹Ba, with a half-life of 12 days, and ⁴⁷Ca, with a half-life of 4.5 days.

If there are initially twice as many calcium atoms as there are barium atoms, what will be the ratio of calcium atoms to barium atoms 2.10 weeks later?

N_Ca/N_Ba = ?

Suppose a crate of mass 8.8 kg is placed on the plank in the figure below at a distance x = 6.3 m from the left end. If the plank has a mass of 12 kg, find the forces exerted by the two supports on the plank. (Indicate the direction with the sign of your answer.)

I need to know the steps of solution for part (b,c,d) I have been trying for almost 2 days.

A 195 -keV X-ray photon coherently scatters off one of the valence electrons of a nitrogen atom. Assume that the scattering angle of the photon is ? = 15

What are the advantages and disadvantages of collecting observational data on a sport skill during a competitive event as opposed to a practice session

Two identical, small insulating balls are suspended by separate 0.21-m threads that are attached to a common point on the ceiling. Each ball has a mass of 7.4 x 10-4 kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, spread apart with an angle of 50 degrees between the threads. Determine (a) the charge on each ball and (b) the tension in the threads.

A 29.3 L sample of air at 31.5% contains 0.275g of water vapor. What is the relative humidity of the air, if the vapor pressure of water at this temperature is 34.8 torr? Answer must contain proper significant figures

A pipe contains water that has a flow rate of 475 gal/min. If water is flowing with a velocity of 2.5m/s, what is the diameter of the pipe in meters? Answer must contain the proper significant figures

A swimming pool of width 9.0m and length 24.0m is filled with water to a depth of 3.0m. Calculate pressure on the bottom of the pool due to the water. Assume that the atmospheric pressure is 741 torr and the density of water is 1.0045g/cm3. Answer must contain the proper significant figures.

Krypton gas (Kr) and an unknown gas are mixed in a container with a small hole in the side. The Kr gas escapes from the container at a rate of 0.882ml/s. The unknown gas escapes from the container at a rate of 1.5256mL/s. What is the molar mass of the unknown gas? If the gas is a diatomic made of two identical atoms, what is the unknown gas? Answer must contain the proper significant figures.

A two dimensional transverse water waves spread in circular ripples a) show that the amplitude at distance r from the intial disturbance is proportional to sqrt of r b) the intensity of the above wave at distant r=2m is 10^-4 W. what is the intensity at 4m distance?

How are radio waves created? And how do they reflect and absorbed?

The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.0240 kg and is moving along the x axis with a velocity of +6.27 m/s. It makes a collision with puck B, which has a mass of 0.0480 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the speed of (a) puck A and (b) puck B. angles: a=65, b=37

An archer shoots an arrow at an angle 20◦ above the horizontal. How far from the archer does the arrow hit the ground if it is shot with a speed of 50 m/s from 1.75m above ground? Hint: Start with setting up your xy coordinates system appropriately.

Extra Practice: An archer standing on a 15◦ slope shoots an arrow 20◦ above the horizontal. How far down the slope does the arrow hit if it is shot with a speed of 50 m/s from 1.75m above ground?

An ancient club is found that contains 189g of carbon and has an activity of 6.66 decays per second. Determine its age in years (do not enter units) assuming that in living trees the ratio of ¹⁴C/¹²C atoms is 1.30×10^-12.

A satellite in a circular orbit around the earth with a radius 1.011 times the mean radius of the earth is hit by an incoming meteorite. A large fragment (m = 75.0 kg) is ejected in the backwards direction so that it is stationary with respect to the earth and falls directly to the ground. Its speed just before it hits the ground is 359.0 m/s.

Find the total work done by gravity on the satellite fragment. R_E 6.37