A spacecraft is traveling with a velocity of vox = 6920 m/s along the +x direction. Two engines are turned on for a time of 844 s. One engine gives the spacecraft an acceleration in the +x direction of ax = 2.29 m/s², while the other gives it an acceleration in the ty direction of ay = 7.89 m/s². At the end of the firing, what is a) vx and b) vy?

A space vehicle is coasting at a constant velocity of 19.3 m/s in the +y direction relative to a space station. The pilot of the vehicle fires aRCS (reaction control system) thruster, which causes it to accelerate at 0.337 m/2 in the + direction. After 59.8 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction.

A boat is docked on the southern shore of a swiftly moving river that is 262.0 m wide. The river flows from east to west with a speed of 4.00 m/s relative to the shore. There is a dock located upstream on the northern side of the river at an angle of 57.0∘57.0∘ relative to the shore (i.e. north of east). The boat is able to travel at a speed of 6.50 m/s relative to the water. If the boat travels directly to the dock on the northern shore at a constant speed, how long does it take to get there?

OK, this is the last time for one of these crazy adventures. THIS time, though, there is a window in the floor, and you can see that you re in a rocket which has just taken off from the surface of an alien planet. By taking careful measurements out that window you determine that the rocket is accelerating upward at 7.42 m/s^2. When you drop a ball from a height of 1.74 m, it hits the floor 0.254 s later. What is the value of g for the alien world below you? 1. 63.8 m/s^2 55.2 m/s^2 3 79.1 m/s^2 4 46.5 m/s^2

A spacecraft is traveling with a velocity of v0x = 6710 m/s along the +x direction. Two engines are turned on for a time of 796 s. One engine gives the spacecraft an acceleration in the +x direction of ax = 2.31 m/s2, while the other gives it an acceleration in the +ydirection of ay = 8.98 m/s2. At the end of the firing, what is a) vx and b) vy?

The instantaneous speed of a particle moving along one straight line isv(t) = ate−5t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)

An athlete crosses a 29 m wide river by swimming perpendicular to the water current at a speed of 1.1 m/s relative to the water. He reaches the opposite side at a distance 45 m downstream from his starting point. w = 29 md = 45 mvs = 1.1 m/s Part (a) How fast is the water in the river flowing with respect to the ground in m/s? Part (b) What is the speed of the swimmer with respect to a friend at rest on the ground in m/s?

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?

How would  I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)

A canoe has a velocity of 0.420 m/sm/s southeast relative to the earth. The canoe is on a river that is flowing at 0.500 m/sm/s east relative to the earth. (Figure 1) Part A Find the magnitude of the velocity  v⃗ CRv→CR of the canoe relative to the river. Express your answer in meters per second.