The elevator rises with an acceleration of 2 m / s ^ 2. at the moment when its speed became equal to 2.4 m / s

The elevator rises with an acceleration of 2 m / s ^ 2. at the moment when its speed became equal to 2.4 m / s, a bolt began to fall from the ceiling of the elevator. elevator height 2.47 m. Calculate the bolt fall time and the distance traveled by the bolt relative to the elevator shaft

Given:
a = 2m / s ^ 2,
v = 2.4m / s,
H = 2.47m;
Find: t -? h -?
Taking the elevator floor as the coordinate reference point at the moment when the bolt starts to fall, we will write how the coordinates of the floor and bolt changed:
y1 = v * t + 1/2 * a * t ^ 2 – floor coordinate;
y2 = H + v * t – 1/2 * g * t ^ 2 – bolt coordinate,
Where
g = 10m / s ^ 2 – free fall acceleration;
At the moment when the bolt touches the elevator floor, their coordinates are:
y1 = y2;
v * t + 1/2 * a * t ^ 2 = H + v * t – 1/2 * g * t ^ 2
We shorten v * t and get an expression for t:
t ^ 2 = (2 * H) / (a ​​+ g) = 4.94 / 12;
t = 0.642s;
Let’s calculate the coordinate of the bolt at this moment in time:
y2 = H + v * t – 1/2 * g * t ^ 2;
Bolt Distance:
h = H – y2 = -v * t + 1/2 * g * t ^ 2 = 0.776m.