A toy rocket is launched from a 1.41.4 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h equals negative 4.9 t squared plus 9.1 t plus 1.4h=-4.9t2+9.1t+1.4. how long will it take for the rocket to hit the ground?

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Physics

29 October, 12:42

A toy rocket is launched from a 1.41.4 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h equals negative 4.9 t squared plus 9.1 t plus 1.4h=-4.9t2+9.1t+1.4. how long will it take for the rocket to hit the ground?

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Sheldon Zavala · Answer 1

In this problem, we are already given the equation for height h in terms of time t. So, the only thing you would do is substitute h and solve for t. If the height is given as 1.414 m, then the solution would be:

h=-4.9t² + 9.1t + 1.4

1.414 = - 4.9t² + 9.1t + 1.4

-4.9t² + 9.1t - 0.014 = 0

Since this is a quadratic equation, there can be two answer for this equation. They are t = 1.859 seconds, - 0.001537 seconds. Since the negative answer is impossible, the answer would be 1.859 seconds.