a rock is vertically upward with a velocity of 10 m/s. calculate the maximum height it reaches and time taken to reach that height.

maximum height: p(t) = Vo * t - 1/2 * g * t^2

p’(t) = v(t) = 0 = Vo - g*t. So, maximum height occurs when t = Vo / g

p(Vo / g) = Vo^2/g - 1/2 * g * (Vo/g)^2

Vo = 10 m / s. Let’s approximate g = 10 m / s^2

p(Vo / g) = 10^2 / 10 - 1/2 * 10 * (10/10)^2 = 10 - 5 = 5 meters (approximately)

Calculation of time:

v = u + gt

0 = 10√2 + (-10)t

-10√2 = -10t

2 = √2s