if you were to kick a rock on mars at a velocity of 56 feet per second from the top of a 30 foot hill and the equation models h=-1.9^2+56t+30 where h is height and t is time.
How high will the rock get of the surface?
the max height is on the axis of symmetry of the parabola
tmax = -b / 2a = -56 / (2 * -1.9)
solve for the time at max
... plug the time into the height equation to find max height
To find how high the rock will get off the surface, we need to determine the maximum height it reaches. The equation given, h = -1.9t^2 + 56t + 30, represents the height of the rock above the surface of Mars at a given time t.
Since the equation is in vertex form (h = a(t - h)^2 + k), we can identify the maximum height by finding the vertex (h, k).
In this case, a = -1.9, which is the coefficient of the t^2 term, and the equation gives us the value of h (30) correctly. To calculate the time at which the rock reaches its maximum height, we can use the formula for the x-coordinate of the vertex, given by t = -b/(2a).
In this case, b = 56, so the time at which the rock reaches its maximum height is t = -56/(2*(-1.9)).
Now, we can plug this value of t back into the equation to find the maximum height (h):
h = -1.9(t^2) + 56t + 30
By substituting t = -56/(2*(-1.9)), we can calculate h:
h = -1.9[(-56/(2*(-1.9)))^2] + 56(-56/(2*(-1.9))) + 30
Evaluating this expression will give us the maximum height reached by the rock on Mars.