An astronaut (mass of 100 kg, with equipment) is headed back to her space station at a speed of 0.750 m/s s but at the wrong angle. to correct her direction, she fires rockets from her backpack at right angles to her motion for a brief time. these directional rockets exert a constant force of 100.0 n for only 0.200 [neglect the small loss of mass due to burning fuel and assume the impulse at right angles to her initial momentum.(a) what is the magnitude of the impulse delivered to the astronaut? (b) what is her new direction (relative to the initial direction) (c) what is her new speed ?

(a) 20.0 Ns

(b) 14.9°

(c) 0.776 m/s

Explanation:

Let's say the astronaut's original velocity is in the x direction.  The impulse from rockets is at a right angle to this, or in the y direction.

(a) Impulse is force times time.

J = (100.0 N) (0.200 s)

J = 20.0 Ns

(b) Impulse is change in momentum.

J = mΔv

20.0 Ns = (100 kg) (vᵧ − 0 m/s)

vᵧ = 0.200 m/s

The angle of the new total velocity, relative to the x direction, is:

θ = atan(vᵧ / vₓ)

θ = atan(0.200 m/s / 0.750 m/s)

θ = 14.9°

(c) The magnitude of the new total velocity is:

v² = vₓ² + vᵧ²

v² = (0.750 m/s)² + (0.200 m/s)²

v = 0.776 m/s

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