Some Kinematics questions with cars and satallites

[neonjr]

Having difficulty with the followingCalculating this collision, as the standard equation does not apply, i don't think.

Question 1:

A 2000kg car traveling at 24 m/s EAST (x), collides with a 3600kg truck traveling at 10m/s SOUTH(y). What is there velocity immediately after impact.

Question 2:

An Earth Satellite travels in a circular orbit of radius 4 times the Earths radius. Calculate its acceleration in m/s^2

Question 3:

A satellite circles the Earth at an average altitude of 760km, with a period of 100 min. Calculate the mass of the Earth, if G = 6.67x10^-11 Nm^2/kg^2, and the radius of the Earth is 6.38x10^6m.


Can you advise me the correct equation to use and directions, I'm lost. Please and thank you.

Josh

 

[tiny-tim]

Welcome to PF!

Having difficulty with the followingCalculating this collision, as the standard equation does not apply, i don't think.
A 2000kg car traveling at 24 m/s EAST (x), collides with a 3600kg truck traveling at 10m/s SOUTH(y). What is there velocity immediately after impact.

Hi Josh! Welcome to PF!

By "standard equation", I take it you mean conservation of momentum in one dimension?

It's ok - you just have two equations instead of one - conservation of momentum North, and conservation of momentum East!

(btw, I suppose you're expected to use conservation of energy as well - but in practice, it wouldn't be conserved, because the vehicles would be deformed in the collision. )

As to Questions 2 and 3: do you know a formula for the aceleration of something in a circle?

 

[Moetasim]

For question 1, we can use the conservation of momentum equation to calculate the velocity after the collision. The equation is: m1v1 + m2v2 = (m1 + m2)v3, where m1 and m2 are the masses of the car and truck respectively, v1 and v2 are their velocities before the collision, and v3 is their velocity after the collision. We can plug in the values and solve for v3. Remember to take into account the direction of the velocities.

For question 2, we can use the equation for centripetal acceleration, which is a = v^2/r, where v is the velocity and r is the radius of the circular orbit. The velocity of the satellite can be calculated using the equation v = 2πr/T, where T is the period of the orbit. Plug in the values and solve for a.

For question 3, we can use the equation for centripetal force, which is F = (mv^2)/r, where m is the mass of the satellite, v is its velocity, and r is the radius of the orbit. We can also use the equation for gravitational force, which is F = (Gm1m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses of the Earth and the satellite respectively, and r is the radius of the Earth. Set these two equations equal to each other and solve for the mass of the Earth, m1.

Remember to always pay attention to the units and directions when solving kinematics problems. I recommend practicing with similar problems and using online resources or textbooks to review the equations and concepts. Good luck!