Given the following data for the planet mars: polar radius 3,389.5 km mass = 6.4171 x 1023 kg g-6.67408 x 101 m/kg s and that the universal gravitational constant is neglecting friction in the thin martian atmosphere, calculate the escape speed for a 10,000 kg spacecraft blasting off from the martian north pole. remember, the escape speed calculation assumes that t spacecraft uses all of its fuel in an initial "blast" and then coasts the rest of the way to "infinity."

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

Which is special about a dc circuit ? a. it has both series and parallel components b. it has only series or only parallel components c. charge moves in a single direction d. charge moves back and forth quickly