Let h(t) denote the height of an object in meters at time t seconds. h'(t) is the velocity of the object at time t seconds, and h''(t) = -9.8m/s^2 is the acceleration of the object due to gravity. Suppose that at time t = 0, the height of the object is h(0) = h0 and the velocity of the object is h'(0) = v0. (Here, h0 and v0 are some constants.)
A. Find a formula for the velocity function h'(t) in terms of the constant v0.
B. Find a formula for the height h(t) in terms of the constants v0 and h0.
A. h'(t) = vo + t h''(t) = vo - 9.8 t
B. h(t) = ho + vo t + 1/2(-9.8) t^2