A rock is dropped from a tree of height 25m into a lake of 5m depth below, the rock then sinks to the bottom of the lake with constant speed of 1.5m/s. What is the total elapsed time?
To find the total elapsed time, we need to consider two parts of the motion: the time it takes for the rock to fall from the tree to the surface of the lake, and the time it takes for the rock to sink to the bottom of the lake.
First, let's calculate the time it takes for the rock to fall from the tree to the surface of the lake.
Using the formula for free fall:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Rearranging the formula, we get:
t = √(2h/g)
Substituting the given values:
h = 25m
g = 9.8 m/s^2
t = √(2 * 25 / 9.8)
t ≈ √5.1
t ≈ 2.26 seconds
Next, let's calculate the time it takes for the rock to sink to the bottom of the lake.
Since the rock is sinking with a constant speed, we can use the formula:
time = distance / speed
The distance the rock needs to sink is the depth of the lake:
distance = 5m
The speed at which the rock is sinking is given as 1.5 m/s.
time = 5 / 1.5
time ≈ 3.33 seconds
Finally, to find the total elapsed time, we add the time it took for the rock to fall to the surface of the lake and the time it took for it to sink to the bottom of the lake:
Total elapsed time = time for falling + time for sinking
Total elapsed time ≈ 2.26 seconds + 3.33 seconds
Total elapsed time ≈ 5.59 seconds
Therefore, the total elapsed time is approximately 5.59 seconds.
find time to drop to water: 4.9t^2 = 25
find time to sink: 1.5t = 5
add 'em up.