Answer:
5.76 seconds
Step-by-step explanation:
We are given;
Position of rock from ground level; h(t) = 9 m
Height of cliff;h_0 = 45 m
Velocity;v_0 = 22 m/s
To solve for the time, we will use the gravity formula which is;
h(t) = (-1/2)gt² + (v_0)t + h_0
Plugging in the relevant values to get;
9 = (-1/2)(9.81)t² + 22t + 45
Subtract 9 from both sides to get;
-4.905t² + 22t + 45 - 9 = 0
-4.905t² + 22t + 36 = 0
Finding the roots of the equation through quadratic formula gives;
t = 5.76 or -1.27
t cannot be negative, so we will use the positive value to get;
t = 5.76 s
Thus, the rock will be 9m from the ground level after 5.76 seconds
