A satellite orbits Mars on a closed orbit with e=0.6 and r₁= 4500 km. Calculate the flight path angle(s) y and velocity vectors v components in the rotating frame (v, and v₁) when r= 10000 km.
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- A newly discovered planet moves in a circular orbit around the star at a constant speed. The direction of the planet's acceleration is:The shuttle orbiter A is in a circular orbit of altitude 200 mi, while spacecraft B is in a geosynchronous circular orbit of altitude 22,300 mi. Find the relative position vector of A to B. Use g0 = 32.23 ft∕sec^2 for the surface-level gravitational acceleration and R = 3959 mi for the radius of the earth.You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of ?o=2.45 km/s�o=2.45 km/s . The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth. With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is ?E=6370000 m�E=6370000 m, the mass of the Earth is ?E=5.98×1024 kg�E=5.98×1024 kg , the acceleration due to gravity on the surface of the Earth is ?=9.81…
- Danielle launches a ball off of a platform of height h with velocity vo at an angle 0 above the horizontal. A wall with a ball-sized hole a height H above the floor, with H > h, is a horizontal distance L = 24.0 m away from Danielle. The difference in height between H and h is one-twelfth of L, and the square of the magnitude of the velocity, v, is three-halves of the product gL. H 1 H – h = h 3 L Determine the two values of 0 that ensure the ball passes through the hole. Submit the larger angle as 0, and the smaller angle as 02.The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of…A jetliner is moving at a speed of 245 m/s. The vertical component of the plane's velocity is 40.6 m/s. Given sin e = 0.165, the angle theta is equal to: Select one: O e = 10.0° e = 9.5° e = 11.5° e = 11.0° O O
- A projectile is shot straight up from the earth's surface at a speed of 1.00×104 km/hr .How high does it go?The orbit of the moon around the earth is approximately circular, with a mean radius of 3.85 x 108 m. It takes 27.3 days for the moon to complete one revolution around the earth. Find the average orbital speed of the moon.An experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by r(t)= R cos(wt)i + R sin(wt)j + vztk R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame. In vector form: A)What is the path of the partical in the moving frame? B)what is the velocity of the particle as a function of time relative to the moving frame? C)What is the acceleration of the particle in each frame? D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?
- A particle travels in a circular orbit of radius r = 143.8 m. Its speed is changing at a rate of at = 16.1 m/s2 at an instant when its speed is v = 45.3 m/s. What is the magnatude of the total aceleration of the particle in m/s^2?Two satellites are in circular equatorial orbits of different altitudes. Satellite A is in a geosynchronous orbit (one with the same period as the earth's rotation so that it "hovers" over the same spot on the equator). Satellite B has an orbit of radius rg = 34 000 km. Calculate the velocity which A appears to have to an observer fixed in B when the elevation angle is (a) O and (b) 90°. The x-y axes are attached to B, whose antenna always points toward the center of the earth (-y-direction). B Answers: TB- N (a) 0=0: Vrel 3418.551 (b) = 90°: Vrel = (i 1265.098 ¡ + i 6555.57 j) km/h i+ ° j) km/hAn object is moving in a circle of radius 10 cm centered on the origin in the xy-plane at a constant speed of 5 m/s. (a) Express the motion of the object as a vector that depends on time, i.e. find F(t).