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Dr. John Paul Stapp was U.S. Air Force officer who studied the effects of extreme deceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s, and was brought jarringly back to rest in only 1.40 s! Calculate his (a) acceleration and (b) deceleration. Express each in multiples of g (9.80 m/s2 ) by taking its ratio to the acceleration of gravity.

Respuesta :

Answer:

a) [tex]a=5.7551 \times g[/tex]

b) [tex]d=20.5539\times g[/tex]

Explanation:

Given:

  • speed of rocket initially, [tex]v_i=0\ m.s^{-1}[/tex]
  • top speed of rocket after acceleration, [tex]v=282\ m.s^{-1}[/tex]
  • time taken to get to the top speed, [tex]t_i=5\ m.s^{-1}[/tex]
  • final speed of the rocket, [tex]v_f=0\ m.s^{-1}[/tex]
  • time taken to get to the final speed after reaching the top speed, [tex]t_f=1.4\ s[/tex]

Now the acceleration:

[tex]a=\frac{v-v_i}{t_i}[/tex]

[tex]a=\frac{282-0}{5}[/tex]

[tex]a=56.4\ m.s^{-2}[/tex]

Now as a fraction of gravity:

[tex]a=\frac{56.4}{9.8}\times g[/tex]

[tex]a=5.7551 \times g[/tex]

Now, the deceleration:

[tex]d=\frac{0-282}{1.4}[/tex]

[tex]d=201.4285\ m.s^{-2}[/tex]

Now as a fraction of gravity:

[tex]d=\frac{201.4285}{9.8}\times g[/tex]

[tex]d=20.5539\times g[/tex]

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