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launch an 950 g model rocket straight up and hit a horizontally moving target as it passes 33.0 m above the launch point. The rocket engine provides a constant thrust of 20.0 N . The target is approaching at a speed of 18.0.At what horizontal distance between the target and the rocket should you launch?

Respuesta :

Answer:

[tex]s=43.6124\ m[/tex] is the horizontal distance between the rocket and the target when the rocket should be launched.

Explanation:

Given:

  • mass of rocket, [tex]m=0.95\ kg[/tex]
  • height of horizontal moving target, [tex]h=33\ m[/tex]
  • constant thrust of rocket, [tex]F=20\ N[/tex]
  • speed of approach of the target, [tex]v_h=18\ m.s^{-1}[/tex]

Now the acceleration of the rocket:

[tex]a=\frac{F}{m}[/tex]

[tex]a=\frac{20}{0.95}[/tex]

[tex]a=21.052\ m.s^{-2}[/tex]

Since this acceleration is acting against the gravity therefore there will be a lesser effective acceleration of the rocket:

[tex]a'=a-g[/tex]

[tex]a'=21.052-9.81[/tex]

[tex]a'=11.242\ m.s^{-2}[/tex]

Now the time taken by the rocket to reach the height of 33 m:

[tex]h=u.t+\frac{1}{2} \times g.t^2[/tex]

where:

[tex]u=[/tex] initial velocity of the rocket [tex]=0\ m.s^{-1}[/tex]

[tex]33=0+0.5\times 11.242\times t^2[/tex]

[tex]t=2.4229\ s[/tex]

Now the distance covered by the target in the above time when the rocket has reached the  height of the target:

[tex]s=v_h.t[/tex]

[tex]s=18\times 2.4229[/tex]

[tex]s=43.6124\ m[/tex] is the horizontal distance between the rocket and the target when the rocket should be launched.

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