Enable contrast version

Tutor profile: Marta R.

Inactive
Marta R.
Maths and Physics Tutor
Tutor Satisfaction Guarantee

Questions

Subject: Astrophysics

TutorMe
Question:

A $$30M_\odot$$ star reaches the end of its life and explodes. A $$10M_\odot$$ black hole is left, and the rest of the star is ejected by the explosion. If the total explosion energy is $$10^{46}J$$ and 10% is converted to the kinetic nergy of the ejecta. What is the initial expansion speed of the supernova remnant after the explosion?

Inactive
Marta R.
Answer:

To solve this problem, we need to set the variables. The ejected mass ($$m_{E}$$) is $$20M_\odot$$ once the star was originally $$30M_\odot$$ and the black hole is $$10M_\odot$$. The efficiency of the explosion ($$ \epsilon$$) is 10% and the supernova energy ($$E_{SN}$$) is $$10^{46}J$$. With the Kinetic Energy formula and calling the initial velocity $$V_{EJ}$$, the formula becomes: $$\frac{1}{2}m_{E}V_{EJ}^{2}=\epsilon \times E_{SN} $$ and rearranging the equation, $$V_{EJ}=({\frac{2\times E_{SN} }{m_{E}} )}^{\frac{1}{2}}$$. Converting from solar masses to KG, (1$$M_\odot$$=2\times 10^{30}KG) we get $$V_{EJ}=7.1\times 10^{3} kms^{−1}$$.

Subject: Physics

TutorMe
Question:

A car is travelling at $$15 ms^{-1}$$. The car accelerates uniformly to $$33 ms^{-1}$$. The car's acceleration is $$1.2 ms^{-2}$$. What is the distance covered while the car is accelerating?

Inactive
Marta R.
Answer:

This problem is solved using S.U.V.A.T. We have $$u=15 ms^{-1}$$, $$v=33 ms^{-1}$$ and$$a=1.2 ms^{-2}$$. The formula we can use is: $$v^{2}=u^{2}+2as$$. Rearraging this, we get, $$s=\frac{v^{2}-u^{2}}{2a}$$. So, $$s=\frac{33^{2}-15^{2}}{2\times1.2}$$=360m. The car covered a 360m distance while accelerating.

Subject: Partial Differential Equations

TutorMe
Question:

Find u(x,y) from the following $$ u_{y} = x^{2}+y^{2}$$

Inactive
Marta R.
Answer:

To find this, we have to first integrate both x and y with respect to y and as it is $$u_{y}$$ there will be a function of x (I will call it f(x)) that will not appear in the above eqaution but has to be accounted for when constructing u(x,y). So, integrating $$x^{2}$$ with respect to y, we get $$x^{2} y$$ and integrating $$y^{2}$$ with respect to y, we get $$ \frac{y^{2}}{3} $$. So $$u(x,y)=x^{2} y+\frac{y^{2}}{3}+f(x)$$ where f(x) is the function of x that is not accounted for in $$u_{y}$$

Contact tutor

Send a message explaining your
needs and Marta will reply soon.
Contact Marta

Request lesson

Ready now? Request a lesson.
Start Lesson

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 Lesson" 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.