Review Conceptual Example 15 before attempting this problem. Two identical pellet guns are fired simultaneously from the edge of a cliff. These guns impart an initial speed of 42.6 m/s to each pellet. Gun A is fired straight upward, with the pellet going up and then falling back down, eventually hitting the ground beneath the cliff. Gun B is fired straight downward. In the absence of air resistance, how long after pellet B hits the ground does pellet A hit the ground?

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davidlcastiblanco davidlcastiblanco · Answer 1 · 2019-11-06T23:29:26+01:00

Answer:

t=6.122s

Explanation:

The time required for pellet to reach the maximum height, so what describe the motion is by

[tex]v_{f}=v_{o}+a*t[/tex]

Given:

[tex]v_{a}=v_{b}=v_{o}=30\frac{m}{s}[/tex]

[tex]a=g=-9.8\frac{m}{s^{2} }[/tex]

To describe the time of A and B it takes from

[tex]t_{a}=t_{1}+t\\t_{a}-t_{b}=t_{1}+t-t\\t_{a}-t_{b}=t[/tex]

So replacing:

[tex]v_{f}=v_{o}-g*t[/tex]

[tex]v_{f}=-v_{o}=-30\frac{m}{s}[/tex]

[tex]-30=30-9.8*t[/tex]

[tex]t=\frac{(-30-30)\frac{m}{s} }{-9.8\frac{m}{s^{2}}}[/tex]

[tex]t=6.122s[/tex]