Gravitational Forces in 2D Practice Problems

Consider a probe of mass 750 kg in a low-Venus orbit (circular orbit A) that needs to move to a higher orbit (circular orbit B) as shown in the figure. To move from orbit A to orbit B, the satellite must travel through an intermediate elliptical orbit known as a transfer orbit. Calculate the work produced by the probe's engine to move the probe from orbit A to the elliptical orbit.

On a basketball court, a basketball player recorded a standing vertical leap of 125 cm. Imagine that this player was given the opportunity to travel to a spherical celestial object in outer space. The mass per unit volume of the celestial object is 2.2 g/cm³. Calculate the maximum radius of the celestial object, allowing the player to escape by jumping vertically.

Four masses, which are called: $m_1=5\ kg$, $m_2=4\ kg$, $m_3=3\ kg$, and $m_4=6\ kg$, are positioned at the corners of a rectangle as shown below. Determine what the $x$ and $y$ components of the gravitational force exerted on mass $m_1$ due to the other three masses will be. Express the force in vector notation using $\hat{i}$ and $\hat{j}$.