An engine of the orbital maneuvering system (OMS) on a

space shuttle exerts a force of for 3.90 s, exhausting
a negligible mass of fuel relative to the 95,000-kg mass of the
shuttle. (a) What is the impulse of the force for this 3.90 s? (b)
What is the shuttle’s change in momentum from this impulse?
(c) What is the shuttle’s change in velocity from this impulse?
(d) Why can’t we find the resulting change in the kinetic energy of
the shuttle?

To find the answers to these questions, we need to use the concepts of impulse, momentum, and kinetic energy. Let's go step by step:

(a) The impulse (J) of a force is given by the product of the force (F) and the time (t) over which the force is exerted. Mathematically, J = F * t. In this case, the given force is exerted for 3.90 seconds. However, you haven't provided the value of the force, so we cannot calculate the impulse without knowing the force.

(b) The change in momentum (Δp) of an object is equal to the impulse applied to it. Mathematically, Δp = J. So, if you have the impulse from part (a), you can calculate the change in momentum of the shuttle.

(c) The change in velocity (Δv) of an object is related to its change in momentum. Since momentum (p) is equal to the product of mass (m) and velocity (v), we can write Δp = m * Δv. Solving for Δv, we get Δv = Δp / m. If you know the change in momentum from part (b) and the mass of the shuttle, you can calculate the change in velocity.

(d) The resulting change in kinetic energy cannot be determined solely from the given information. The kinetic energy (K) of an object is given by the equation K = (1/2) * m * v^2, where m is the mass and v is the velocity. To find the change in kinetic energy, you need to know the initial and final velocities. Since only the change in velocity is given in part (c), we cannot directly calculate the change in kinetic energy.

In summary, without knowing the force exerted by the engine, it is not possible to determine the impulse, change in momentum, change in velocity, or change in kinetic energy of the shuttle.