A radar station locates a sinking ship at range 19.5 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 166° clockwise from north, with elevation 1.95 km.

(a) Write the displacement vector from plane to ship, letting î represent east, ĵ north, and k up.

(b) How far apart are the plane and ship? 2 km

A child hits an ice cube with a mass of 10 grams on a table with a force of 10 N. The impact lasts 0.02 seconds. The ice cube flies off the table, which is 1 meter high and lands some distance away. Assume there is no friction between the ice cube and the table.

a. What is the velocity of the ice cube when it leaves the table?

b. What is the final velocity of the ice cube just before it hits the floor?

c. What is the momentum of the ice cube just before it hits the floor?

d. What distance will the ice cube land from the foot of the table?

e. Suppose the ice cube had broken into two pieces just after the child hit the ice and moved away from each other while falling to the floor. How would the total momentum of the two pieces just before they hit the floor compare to the momentum you found in part (c)?

An inclined plane is sliding, and accelerating, on a horizontal frictionless surface. There is a block at rest on the sloping surface, held in place by a static friction through the horizontal acceleration of the system. the coefficient of static friction between the block and the inclined plane is 0.615. the slope of the incline plane is 42.5 degrees with respect to the horizontal.

a) What is the minumum acceleration of the inclined plane for the square block not to slide?

I found a=1.891 m/s^2

b) what is the maximum acceleration of the inclined plane for the square block not to slide?

To apply the concept of base of support, have a partner stand with his or her feet together and see how much force you must apply to move him or her off balance. Then, have your partner stand with the feet farther apart and repeat your attempts to push him or her off balance. Explain the concept behind how the two differ and how a patient would use this concept if he had balance difficulties and did not use assistive devices to walk

In your own words explain why the force and acceleration vectors in Uniform Circular Motion point inward. Also discuss the differences between Centripetal Force and Centrifugal Force.

Two masses, m1 and m2, are falling but not freely. In addition to gravity, there is also a force F1 applied directly to m1 in the downward direction and a force F2 applied directly to m2 in the horizontal direction. Friction (µs) is present between the two masses and the forces are applied such that they do not rotate. The force F2 is as large as it can be and not have m2 slide relative to m1. (a) Find an expression for the acceleration of the center of mass of the m1 + m2 system in terms of m1, m2, F1, F2, and g? (b) Draw a FBD for each mass separately. Identify motion constraints and Newton's 3rd law force pairs. (c) Write down Newton's 2nd law applied to each mass separately. (d) If both masses are each 2 kg, the coefficient of static friction between the surface is µs = 1/2, and F1 = 25 N, What is the value of F2?

The optimal x-ray energy for producing high contrast images is approximately in the range 20-40 keV. In terms of what we know about how x-rays interact with atoms, discuss the main mechanisms that determine this optimal range and what happens to the images for energies outside this range.?

In one measurement the following values were obtained :

mass of the substance: M=1.3kg,

Power used : P=8.1W

Slope of the Temp vs Time: S=0.027 ^oC/sec.

Knowing that the error on each measured value was 5%

the error on specific heat capacity is (in J/(kg ^oC)

(values may be non-physical )

Determine the following rotational quantities. Make assumptions or estimates where appropriate.

A) What is the magnitude of the angular velocity of the Earth in its orbit around the Sun?

B) What is the magnitude of the angular velocity of a wheel in a car driving on the interstate. (state all assumptions)

C) What is the magnitude of the angular acceleration of a gyroscope that starts out spinning at 53 Hz and takes 7.2 s to slow down to zero?

D) A spinning neutron star, with a period of 4.3 ms, is slowing with an angular acceleration of 2.4x10-8 s-2. How many years will it take for it to stop spinning?

4. A car of mass m is traveling with constant speed v around a circular banked road of radius R, see the

side view and the free-body diagram.
a) Apply Newton’s 2nd law to the car, i.e. write equations for the centripetal, angular, and vertical components of the net force.
b) Determine the angle θ at which the road should be banked so that no static friction is required to drive the car.
Now, include the static friction force FS in the free-body diagram and Newton’s equations.
c) Find the maximum speed vmax at which the car can travel around without slipping. Assume the coefficient of maximum static friction is μs.
In the end, find the expressions for the contact force with which the ground is acting on the car, i.e.:
d) The magnitude of the normal force FN and
e) The magnitude of the static friction FS, in terms of the given quantities m, v, R, g, and θ.

A physics instructor wants to project a spectrum of visible-light colors from 400 nm to 700 nm as part of a classroom demonstration. She shines a beam of white light through a diffraction grating that has 600 lines per mm, projecting a pattern on a screen 2.9 m behind the grating.

How wide is the spectrum that corresponds to m = 1? Express your answer with the appropriate units.

How much distance separates the end of the m = 1 spectrum and the start of the m = 2 spectrum?

a 1.0 x 10³ kg toyota collides into the rear end of a 2.2 x 10³ kg cadillac stopped as a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer,knowing that the coefficient of kinetic friction between the tires and the road was .4 calculated the speed of the toyota at impact. What was that speed? Please show the steps that got you to the answer as that is what I am interested in! thanks

As simply as you can but with complete and comprehensive detail, state and explain each of Newtons Three Fundamental Laws of Motion. After you have explained all Three Laws look come up with and explain an example problem of your own. It must include an explanation of how at least one of Newton's laws is used if not more than one. (can not use online sites)