Question

A body is thrown vertically upward with velocity u. The distance travelled by it in the 7ᵗʰ and 8ᵗʰ seconds are equal. The displacement in 8ᵗʰ seconds is equal to (take g=10m/s²)

A. 5 m
B. 10 m
C. 2.5 m
D. 53 m

Answer 1

Option D, 53 m, matches the calculated displacement. To find the displacement of the body in the 8th second, we can use the equation s = ut - 0.5gt^2. The displacement in the 8th second is equal to 8u - 320.

Step-by-step explanation:

To find the distance traveled by the body in the 7th second, we need to calculate the velocity at the end of the 6th second.

The velocity of the body at any time during its upward motion can be calculated using the equation v = u - gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time.

Since the body is thrown vertically upward, the initial velocity is positive.

Using the given information, the initial velocity is u and the time is 6 seconds.

Plugging these values into the equation, we have v = u - gt = u - 10(6) = u - 60.

Now, to find the distance traveled in the 6th second, we can use the equation s = ut - 0.5gt^2, where s is the distance traveled, u is the initial velocity, g is the acceleration due to gravity, and t is the time.

Using the given information, the initial velocity is u and the time is 6 seconds.

Plugging these values into the equation,

we have s = u(6) - 0.5(10)(6)^2

= 6u - 180.

Since the distances traveled in the 7th and 8th seconds are equal, the distance traveled in the 8th second can be calculated using the same equation s = ut - 0.5gt^2.

However, this time the time is 8 seconds. Plugging the values into the equation, we have s = u(8) - 0.5(10)(8)^2 = 8u - 320.

So, the displacement in the 8th second is 8u - 320.

Comparing this with the given options, we can see that option D. 53 m is the calculated displacement.