When a body falls from rest its distance from the starting point varies as the square of the time it has been falling : if a body falls through $402 \frac{1}{2}$ feet in $5$ seconds, how far does it fall in $10$ seconds? Also how far does it fall in the $10^{t h}$ second?

Open in App

Solution

Let $d$ be the distance from starting point and $t$ be the time, then according to question

$d = k t^{2}$

Given $d = 402.5$ for $t = 5$ . So,

$402.5 = k {.5}^{2}$

$k = \frac{402.5}{25} = 16.1$

So,

$d = (16.1) t^{2}$

For $t = 10$

$d = (16.1) 100 = 1610$ feets

and distance for $t = 9$

$d = (16.1) 81 = 1304.1$ feets

Distance fallen in $10 t h$ second =distance at $t = 10$ - distance at $t = 9$

$= 1610 - 1304.1 = 305.9$ feets

Suggest Corrections

Similar questions

Q. The distance through which a body falls from rest varies as square of time it takes to fall that distance. It is known that the body falls

64 c m

2

seconds. How far does that body fall in

6

seconds?

Q. A body falls from rest. In the last second of its fall it covers half of the total distance. If g is 9.8

m / s^{2},

then the total time of its falls is (in second) ?

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time;

Q. A body falls from rest. In the last second of its fall n coven half of the total distance. If g is

9.8 m / s^{2}

, then the total time of its fall is (in second)

Q. A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of ( in seconds upto two decimals)

Join BYJU'S Learning Program

When a body falls from rest its distance from the starting point varies as the square of the time it has been falling : if a body falls through 40212 feet in 5 seconds, how far does it fall in 10 seconds? Also how far does it fall in the 10th second?

When a body falls from rest its distance from the starting point varies as the square of the time it has been falling : if a body falls through $402 \frac{1}{2}$ feet in $5$ seconds, how far does it fall in $10$ seconds? Also how far does it fall in the $10^{t h}$ second?