You are controlling a satellite with a mass of 300 kg. The main and lateral thrusters can exert the forces shown. How long do you need to run each of the thrusters to achieve the final velocity as shown in the diagram? Assume the satellite has zero initial velocity.

The figure shows a system composed of two bodies, of masses mi and m2, connected through an ideal rope that passes through a pulley, also ideal. Both bodies are on two inclined planes, with the same angle of inclination 0, and coefficients of friction 1 and 2. If mi < m2, find the acceleration of the system. m₂

Body U with mass 5m is stacked on the top body W with mass m, and released. The bodies are in contact along the frictionless interface at 45° to the vertical. The body U is in contact with the frictionless vertical wall. Body W lies on the floor with coefficient of friction u. Relevant dimensions are shown in the figure. Express the results in terms of given quantities: m, g, h and µ (except when µ is given numerically). You need not evaluate sin 45° = cos 45° = 2/2. h U: 5m C 45 D W: m 3h

A projectile object reaches a height of 430 m, if it is fired straight up using a spring-loaded gun. Using the same gun, what is the maximum height (m) that can be reached by the projectile if it fired at an angle of 31 ° from the vertical?