In above problem ratio of distance traveled in first second of upward motion to first second of downward motion is

Options

A. `1:7`
B. `5:3`
C. `9:1`
D. `3:5`

Answer

To solve the problem of finding the ratio of the distance traveled in the first second of upward motion to the first second of downward motion, we can follow these steps:

### Step 1: Identify the parameters for upward motion
- Initial velocity (u) = 50 m/s (upward)
- Acceleration (a) = -10 m/s² (due to gravity, acting downward)
- Time (t) = 1 second

### Step 2: Calculate the distance traveled in the first second of upward motion
Using the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]

Substituting the values:
\[ s = (50 \, \text{m/s})(1 \, \text{s}) + \frac{1}{2}(-10 \, \text{m/s}^2)(1 \, \text{s})^2 \]
\[ s = 50 - 5 \]
\[ s = 45 \, \text{meters} \]

### Step 3: Identify the parameters for downward motion
- Initial velocity (u) = 0 m/s (the body starts from rest at the maximum height)
- Acceleration (a) = 10 m/s² (downward)
- Time (t) = 1 second

### Step 4: Calculate the distance traveled in the first second of downward motion
Using the same equation:
\[ s = ut + \frac{1}{2} a t^2 \]

Substituting the values:
\[ s = (0 \, \text{m/s})(1 \, \text{s}) + \frac{1}{2}(10 \, \text{m/s}^2)(1 \, \text{s})^2 \]
\[ s = 0 + 5 \]
\[ s = 5 \, \text{meters} \]

### Step 5: Calculate the ratio of distances
Now, we can find the ratio of the distance traveled in the first second of upward motion to the first second of downward motion:
\[ \text{Ratio} = \frac{\text{Distance upward}}{\text{Distance downward}} = \frac{45 \, \text{meters}}{5 \, \text{meters}} = 9 \]

Thus, the ratio of the distance traveled in the first second of upward motion to the first second of downward motion is:
\[ \text{Ratio} = 9:1 \]

### Final Answer:
The ratio of distance traveled in the first second of upward motion to the first second of downward motion is \( 9:1 \).

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