Congratulations on getting the answer to the second question.
Now, let's try to iron the wrinkles in the first problem.
The problem gives you the value for r. This is 2.1 km = 2,100 m. It also gives you the time it takes for the car to make one full lap around the track.
To get the...
What do you know about the net force in the x and y directions?
I would start by writing a sums of forces equation for the x direction and a sums of forces equation for the y direction. From here, see what you can algebraically manipulate to get what you want.
For the first question:
2.1 km is the radius of the track. You need to use this information to find the entire length of the track (more specifically, the circumference). Then use this information to find the velocity.
For the second question:
As you said, the force is 5 times the weight...
Start by drawing all four charges and then draw a force diagram for the charge of interest. You will probably find that you run into a bit of trigonometry.
I believe you miscalculated the velocity in the first question. You probably want to give this another look.
In the second question, try rewriting
F -mg = m(v^2)/r all in terms of m, g, v, and r.
Then go through and see what you can cancel.
You will not an answer so easily on this website. For one, this should be posted in the homework section of the site, but secondly, and perhaps more importantly, you must provide an attempt at a solution before I (or, hopefully, anyone else) will help you.
The initial velocity of the gas would be zero with respect to the probe. Consider the total momentum of the proble + gas system. It is this vector quantity that remains unchanged.
It would be beneficial to approach this problem from an energy standpoint. How much energy was added to the system by raising the car up to 50 m? What subsequently happened to that energy? Where did it go?
1/2 mv^2 gives the kinetic energy of an object with mass m moving with velocity v. To find the change in kinetic energy, one would have to solve for Kfinal - Kinitial, which would be equal to the Wtotal of which you speak.