Question

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for

Answer 1

5 Seconds

The Formula used to calculate the distance covered in nth second:

Sn = ut + 1/2a(2n -1)

Calculating the first distance(s1) using the formula mentioned above:

= g/2(2 x 1 - 1)

= 10/2(2 x 1 - 1)

= 5 (1)

= 5 meters

Calculating the second distance (s2) using the formula mentioned above:

= g / 2 (2 x 2 - 1)

= 10/2(4 - 1)

= 5 (3)

= 15 meters

Calculating the third distance (s3) using the formula mentioned above:

= g / 2 (2 x 3 - 1)

= 10/2 (6 - 1)

= 5 (5)

= 25 meters

Adding all the distances which we obtained we get:

= 5 + 15 + 25

= 45 meters

Now calculating time taken:

g / 2(2T - 1) = 45

Substituting all the known values into this equation we get:

5(2T - 1) = 45

10T - 5 = 45

10T = 50

T = 50 / 10

T = 5 seconds

Therefore, the time the stone remains in the air is for 5 seconds.