TutorMe homepage

SIGN IN

Start Free Trial

Nick V.

Undergraduate Student at MIT

Tutor Satisfaction Guarantee

Physics (Newtonian Mechanics)

TutorMe

Question:

If a rock is thrown off the side of a cliff 80m high with an initial speed of 30 m/s in the horizontal direction, what is the rock's speed at the bottom of the cliff (just before impact)?

Nick V.

Answer:

Since the initial speed is entirely horizontal, finding the vertical component of the speed at the bottom has the initial condition of starting at 0 m/s in the vertical direction. Therefore using vf^2=vo^2 + 2gy, where vo is zero, g is 10 m/s^2, and y is 80m, vf is calculated then to be 40m/s in the vertical direction. As for the horizontal component of the rock's velocity, there is no horizontal acceleration of the rock (ignoring air resistance), making the final horizontal speed still 30m/s. To find the resultant speed, the horizontal and vertical speeds must be added vectorally, which can be done with the pythagorean theorem since they form a right triangle. Therefore v^2=30^2 + 40^2, leaving the final speed at 50 m/s.

Physics (Electricity and Magnetism)

TutorMe

Question:

A Point charge of charge +Q resides in the center of a hollow regular tetrahedron of side length a. Find the outward flux through one of the faces of the tetrahedron.

Nick V.

Answer:

Using Gauss's Law, the total flux from an enclosed charge is equal to q/ε. Since the tetrahedron symmetrically encloses the point charge, we can say that 1/4th of the total flux goes through each face of the shape, since there are 4 faces in a tetrahedron. From this, the flux through one face must be (+Q/ε)*(1/4)= +Q/(4ε) where ε is the permittivity of free space.

Calculus

TutorMe

Question:

Using the Divergence Theorem, find the flux of the velocity field F=<x,y,z> through the surface f(x,y)=4-x^2-y^2 bounded by the x-y plane.

Nick V.

Answer:

The divergence Theorem states that the flux surface integral of a vector valued function over a closed surface is equivalent to the Volume integral of the divergence of the function over the volume enclosed by the given surface. ∯〖F(x,y,z)dS 〗=∰∇⋅F dV The divergence of this function is the sum of the partial derivatives with respect to each variable, so 1+1+1=3. Evaluating the triple integral where z ranges from 0 to 4-x^2-y^2, and x and y are converted to polar coordinates, r ranges from 0 to 2 and θ ranges from 0 to 2π. Evaluating this triple integral gives ∬3(4-r^2 )rdrdθ. Evaluating the next integral gives 12∫_0^2π▒dθ=24 π.

Send a message explaining your

needs and Nick will reply soon.

needs and Nick will reply soon.

Contact Nick

Ready now? Request a lesson.

Start Session

FAQs

What is a lesson?

A lesson is virtual lesson space on our platform where you and a tutor can communicate.
You'll have the option to communicate using video/audio as well as text chat.
You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.

How do I begin a lesson?

If the tutor is currently online, you can click the "Start Session" button above.
If they are offline, you can always send them a message to schedule a lesson.

Who are TutorMe tutors?

Many of our tutors are current college students or recent graduates of top-tier universities
like MIT, Harvard and USC.
TutorMe has thousands of top-quality tutors available to work with you.

Made in California

© 2018 TutorMe.com, Inc.