Question

From top of buliding 16 m high droplets fall at regular time interval such that when first drop reaches ground drop 5 starts to fall .dst btw succesive drops is?

a 8,4,2,1
b)7,53,2,1
d)7.5,5,2.5

Answer 1

Let's solve this problem step by step.

We know that the first droplet takes a certain amount of time to reach the ground from a height of 16 m. We can calculate this time using the formula for the time taken to fall freely under gravity.

The formula is given as:

s = (1/2) * g * t^2,

where s is the distance or height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.

Rearranging the formula, we have:

t^2 = (2 * s) / g.

For the first droplet, substituting the values:

t^2 = (2 * 16) / 9.8,

t^2 = 32 / 9.8,

t^2 ≈ 3.27.

So, the time taken for the first droplet to reach the ground is approximately sqrt(3.27) seconds.

Now, we are given that the time interval between each successive droplet is the same. Therefore, to find the time between the first and fifth droplets, we multiply the time taken for one droplet (sqrt(3.27)) by 4, as there are four droplets in between.

So, the time interval between the first and fifth droplets is approximately 4 * sqrt(3.27) seconds.

However, the problem asks for the distance between successive drops, not the time interval. The distance between successive drops can be found by multiplying the time interval by the average velocity of the falling droplets.

The average velocity of a falling droplet can be calculated as:

v = s / t,

where v is the velocity, s is the distance or height, and t is the time.

Using this formula, we can find the average velocity of the first droplet by dividing the height (16 m) by the time taken (sqrt(3.27)).

v = 16 / sqrt(3.27).

So, the average velocity of the first droplet is approximately 8.83 m/s.

Now, let's calculate the distance (dst) between each successive droplet.

dst = v * t,

where v is the average velocity and t is the time interval.

For the time interval between the first and fifth droplets (4 * sqrt(3.27)), the distance would be:

dst = 8.83 * 4 * sqrt(3.27).

Calculating this gives us an approximate distance of 58.92 m.

Therefore, none of the given options a), b), or d) match the calculated distance of 58.92 m.

Based on the calculations above, the correct answer would be:

c) None of the above.