2022-03-30
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asked 2021-02-06

Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a 1.50 kg ball swings downward and strikes a 4.60kg ballthat is at rest, as the drawing shows. a. using the principle of conservation of mechanicalenergy,find the speed of the 1.50 kg ball just before impact b. assuming that the collision is elastic, find the velocities( magnitude and direction ) of both balls just after thecollision c. how high does each abll swing after the collision, ignoringair resistance?

asked 2021-04-25

Flux through a Cube (Eigure 1) A cube has one corner at the origin and the opposite corner at the point (L, L, L). The sides of the cube are parallel to the coordinate planes image
image

asked 2020-10-23

A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.200 kg, and its center of gravity is located tits geometrical center. On the tray is a 1.00 kg plate of food and a 0.190 kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.
image

asked 2020-11-22

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between bat and ball is 1.00×103 s,calculate the average force between the bat and ball during contest.

asked 2022-04-06
What molality of a nonvolatile, nonelectrolyte solute is needed to raise the boiling point of water by 7.10 C   ( K b = 0.520 C / m ) ?
asked 2022-06-06
In AoPS' (Art of Problem Solving) proof of Muirhead's inequality, how does the below equality work out?
The below equation appears to show two expressions (1 and 2), each under the symmetric sum notation, being multiplied together to produce expression 3, which is also under the symmetric sum notation...
but normally, [ A 1 + A 2 ( ) + A n ] [ B 1 + B 2 + ( ) + B n ] is not [ A 1 B 1 + A 2 B 2 + ( ) + A n B n ] ,
that is, when we multiply the sum of A i ( i = [ 1 ,   n ] ) and B i ( i = [ 1 ,   n ] ), the result is not the sum of A i B i ( i = [ 1 ,   n ] )
asked 2021-09-04
The probability that a student owns a car on a college campus is 65% the probability that a student owns a computer is 82% and the probability that a student owns both is 55%.
What is the probability that a student randomly selected owns a car or computer?
What is the probability that a randomly selected student does not own a car or computer?

New questions

Find all triangles with a fixed base and opposite angle
I have a situation where I know the cartesian coordinates of the 2 vertices of a triangle that form its base, hence I know the length of the base and this is fixed.
I also know the angle opposite the base and this is also fixed.
Now what I want to do is figure out how to compute all possible positions for the third vertex.
My maths is rusty, I reverted to drawing lots of pictures and with the help of some tracing paper I believe that the set of all possible vertices that satisfies the fixed base and opposite angle prescribes a circle or possibly some sort of ellipse, my drawings are too rough to discern which.
I started with a simple case of an equilateral triangle, with a base length of two, i.e. the 3rd vertex is directly above the x origin, 0, base runs from -1 to 1 along the x-axis
then i started drawing other triangles that had that same base, -1 to 1 and the same opposite angle of 60 degrees or pi/3 depending on your taste
now i need to take it to the next step and compute the x and y coordinates for all possible positions of that opposite vertex.
struggling with the maths, do i use the sin rule, i.e. sin a / = sin b / B and so on, or do I need to break it down into right angle triangles and then just use something along the lines of a 2 + b 2 = c 2
ultimately, I intend to plot the line that represents all the possible vertex positions but i have to figure out the mathematical relationship between that and the facts, namely,
base is fixed running from (-1,0) to (1,0) angle opposite the base is 60 deg
I then need to extend to arbitrary bases and opposite angles, but thought starting with a nice simple one might be a good stepping stone.