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if a firework on the fourth of july is fired upwards from the ground with an initial speed of 200 m/s...
a. What is the total time the rocket spends ascending towards the sky?
b. How high up from the ground does the rocket travel?

Respuesta :

onyebuchinnaji

(a) The time spent by the rocket ascending towards the sky is 20.4 s.

(b) The height traveled by the rocket from the ground is 2,040.8 m.

The given parameters:

  • initial speed of the firework, [tex]v_o[/tex] = 200 m/s

The time spent by the rocket ascending towards the sky is calculated as follows;

[tex]v_f = v_0 -gt[/tex]

where;

[tex]v_f[/tex] is the final velocity of the rocket at the maximum height

[tex]0 = v_0 -gt\\\\gt = v_0\\\\t = \frac{v_0}{g} \\\\t = \frac{200}{9.8} \\\\t = 20.4 \ s[/tex]

The height traveled by the rocket from the ground is calculated as follows;

[tex]h = v_0t - \frac{1}{2} gt^2\\\\h = 200(20.4) \ - \ \frac{1}{2} (9.8)(20.4)^2\\\\h = 2,040.8 \ m[/tex]

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