Question

A stone is dropped from the top of the tower and travels 24.5 m in the last second of its journey. The height of the tower is ______.

(g = 9.8 m/s²)

Options

• 44.1 m

• 49 m

• 78.4 m

• 72 m

Answer 1

A stone is dropped from the top of the tower and travels 24.5 m in the last second of its journey. The height of the tower is 44.1 m.

Explanation:

Given:

• A stone is dropped (so initial velocity u=0u = 0u=0)
• It travels 24.5 m in the last second of its journey.
• Acceleration due to gravity, g = 9.8 m/s²
• We must find the total height (H) of the tower.

Step 1: Formula for distance fallen in t seconds

S = `1/2`gt²

Step 2: Distance covered in the last second

`S_t = 1/2"gt"^2 - 1/2g(t - 1)^2`

Simplify:

`S_t = 1/2g[t^2 - (t - 1)^2]`

`S_t = 1/2g[t^2 - (t^2 - 2t + 1)] = 1/2g(2t - 1)`

Step 3: Substitute given values

24.5 = `1/2 xx 9.8 xx (2t - 1)`

24.5 = 4.9 (2t − 1)

`(24.5)/(4.9) = 2t - 1`

5 = 2t − 1

2t = 6

t = 3seconds

Step 4: Total height

H = `1/2"gt"^2 = 1/2 xx 9.8 xx 3^2`

H = 4.9 × 9 = 44.1m

44.1 m