Vertical upward lunch (8289)

, por F_y_Q

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A body is launched vertically upwards with an initial velocity of 70\ m\cdot s^{-1}. How long will it take to reach its maximum height?

P.-S.

Since it is a vertical upward launch, if you take the initial velocity as positive, the gravitational acceleration must be negative. The velocity of the object at any instant can be obtained from the expression:

\color[RGB]{2,112,20}{\bm{v = v_0 - gt}}

The condition for the body to stop ascending is that the velocity is zero; at that moment, it will have reached its maximum height. By imposing this condition on the previous equation, you can solve for the time and calculate it:

g\cdot t = v_0\ \to\ {\color[RGB]{2,112,20}{\bm{t = \frac{v_0}{g}}}} = \frac{70\ \frac{\cancel{m}}{\cancel{s}}}{9.8\ \frac{\cancel{m}}{s\cancel{^2}}}= \fbox{\color[RGB]{192,0,0}{\bf 7.14\ s}}