From the top of a tower, 80m high from the ground a stone is thrown in the horizontal direction with a velocity of `8 ms^(1)`. The stone reaches the ground after a time t and falls at a distance of d from the foot of the tower. Assuming `g=10ms^(2)`, the time t and distance d are given respectively by

Options

A. 6s,64m
B. 6s,48m
C. 4s,32m
D. 4s,16m

Explanation

To solve the problem step by step, we will analyze the motion of the stone thrown from the tower. The stone is thrown horizontally, and we need to determine the time it takes to reach the ground and the horizontal distance it travels.

### Step 1: Determine the time of flight (t)

The stone is thrown from a height (h) of 80 meters. The only force acting on the stone in the vertical direction is gravity (g), which is given as \(10 \, \text{m/s}^2\).

Using the formula for the time of free fall:
\[ h = \frac{1}{2} g t^2 \]
we can rearrange this to solve for \(t\):
\[ t^2 = \frac{2h}{g} \]

Substituting the values:
\[ t^2 = \frac{2 \times 80}{10} \]
\[ t^2 = \frac{160}{10} = 16 \]
\[ t = \sqrt{16} = 4 \, \text{seconds} \]

### Step 2: Calculate the horizontal distance (d)

The horizontal distance \(d\) traveled by the stone can be calculated using the formula:
\[ d = u \cdot t \]
where \(u\) is the initial horizontal velocity. Given that \(u = 8 \, \text{m/s}\) and we have found \(t = 4 \, \text{s}\):
\[ d = 8 \cdot 4 = 32 \, \text{meters} \]

### Final Answer

Thus, the time \(t\) and the distance \(d\) are:
- Time \(t = 4 \, \text{s}\)
- Distance \(d = 32 \, \text{m}\)

### Summary

The final answer is:
- \(t = 4 \, \text{s}\)
- \(d = 32 \, \text{m}\)