Unless you need the player to push things around and by physics, you mean just jumping, then implementing jumping as in traditional sidescrollers is simple.
You might want to do something like this:
float currentYspeed;
float GRAVITY = 5;
bool playerFlying;
// In Update():
if (isUpArrowKeyDown() && !playerFlying) { playerFlying = true currentYspeed = 50; }
playerY += currentYspeed;
currentYspeed -= GRAVITY;
if (playerCollidesWithFloor())
{
currentYspeed = 0; // We came back to ground.
playerFlying = false;
}
else if (playerCollidesWithSomethingElse())
{
currentYSpeed = 0; // We hit obstacle in-air.
}
Of course, you might want to refactor and beautify this code, make the position and velocity changes dependent on seconds elapsed etc.
If you don't know how to implement the collision functions, consider reading up on keywords "2D collision detection" or "sidescroller/platformer tutorial".