To find the derivative of the function h(t) that describes the height of the object at a given time, we need to differentiate the function with respect to time (t). The derivative of h(t) is denoted as h'(t) or dh(t)/dt.
Let's assume the upward direction as positive. The initial velocity (u) is given as 120 m/s, and the acceleration due to gravity (g) is approximately 9.8 m/s² (assuming no air resistance).
The height function h(t) can be described by the equation: h(t) = u*t - (1/2)gt²
Differentiating h(t) with respect to t, we can find h'(t) or dh(t)/dt: h'(t) = u - g*t
In this case, the initial velocity u = 120 m/s, and the acceleration due to gravity g = 9.8 m/s².
Therefore, the derivative of the function h'(t) that describes the height of the object at a given time is: h'(t) = 120 m/s - 9.8 m/s² * t