Astudent standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 21 m/s at an angle θ = 28 ° below horizontal. the stone moves without air resistance; use a cartesian coordinate system with the origin at the stone's initial position. (a) with what speed, vf in meters per second, does the stone strike the ground? (b) if the stone had been thrown from the clifftop with the same initial speed and the same angle, but above the horizontal would its impact velocity be different?

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.