Question

A ball is  dropped from the height of 80 m. This distance travelled by the ball in 4th second is _________
1. 50 m
2. 15 m
3. 80 m
4. 35 m

Answer 1

Correct Answer - Option 4 : 35 m

Concept:

Free Fall

• A body is said to be in free fall if it is only accelerating under influence of gravity.
• If a body is just left from a height h, and is made to fall free, it will be experienced only by gravity if we neglect the air resistance.
• The body falls under influence of acceleration due to gravity g which is having an approx value of 10 m s ^-2 . 

Equations of Motion under gravity

• The following three equations are considered under motion in a straight line when there is a uniform acceleration.

v = u + gt        ---(1)

\(h = ut + \frac{1}{2}gt^2\)        ---(2)

v2 = u2 + 2gh        ---(3)

u is initial velocity, v is final velocity, a is acceleration, t is the time interval, h is the height 

Calculation:

Here, we have to find the distance traveled by the ball in 4^th second, that is between distance covered in 4 seconds, subtracted by distance covered in 3 seconds.

The ball was just dropped, so initial velocity was u = 0 m / s

Height covered in 3 seconds t = 3

\(h = (0) \times 3+ \frac{1}{2}(10) \times 3^2 = 45 \ m\)

Height covered in 4 seconds t = 4

\(h' = (0) \times 34+ \frac{1}{2}(10) \times 4^2 = 80 \ m\)

Height convered in 4^th second, h' - h = 80 m - 45 m = 35 m

So, the correct option is 35 m.