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Math  /  Algebra

Questionastronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this knowledge to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured by a nearby observer. (c) Discuss how this would affect the measurement of the astronaut's acceleration. Propose a method by which recoil of the vehicle is avoided.
28. In Figure 5.4.3, the net external force on the 24−kg24-\mathrm{kg} mower is given as 51 N . If the force of friction opposing the motion is 24 N , what force F '(in newtons is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s1.5 \mathrm{~m} / \mathrm{s} when the force FF is removed. How far will the mower go before stopping?

Studdy Solution
To find the stopping distance, use the kinematic equation: v2=u2+2as v^2 = u^2 + 2as
Where: - v=0 m/s v = 0 \, \text{m/s} (final velocity) - u=1.5 m/s u = 1.5 \, \text{m/s} (initial velocity) - a=−1 m/s2 a = -1 \, \text{m/s}^2 (acceleration) - s s is the stopping distance
Substitute the known values: 0=(1.5)2+2(−1)s 0 = (1.5)^2 + 2(-1)s
Solve for s s : 0=2.25−2s 0 = 2.25 - 2s 2s=2.25 2s = 2.25 s=2.252=1.125 m s = \frac{2.25}{2} = 1.125 \, \text{m}
The force exerted by the person is 75 N 75 \, \text{N} and the stopping distance is 1.125 m 1.125 \, \text{m} .

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