A scientist wants to place a satellite into orbit around Earth. Take Earth's mass to be 5.975 1024kg and radius to be 6.371 106 m. (a) If the scientist wants the radius of the orbit to be 7 106 m:
i. What is the speed of the satellite?
ii. What is the period of the orbit?
(b) If the scientist wants the period of the orbit to be 1 day
i. What must the radius of the orbit be?
ii. What is the speed of this orbit?

=force × distance a. work b. velocity c. pressure d. momentum

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when you push the platform, you compress the springs. you do an amount of work of 79.0 j when you compress the springs a distance of 0.230 m from their uncompressed length. (a) what magnitude of force must you apply to hold the platform in this position? (b)how much additional work must you do to move the platform a distance 0.230 m farther? (c) what maximum force must you apply to move the platform a distance 0.230 m farther?