A ball is thrown up under gravity . Find its velocity after 1.0 sec at a height of 10m

Options

A. `5m//s^2`
B. `5m//sec`
C. 10m/sec
D. 15m/sec

Explanation

To solve the problem of finding the velocity of a ball thrown upwards after 1 second at a height of 10 meters, we can follow these steps:

### Step 1: Identify the known values
- Displacement (s) = 10 m (upward)
- Time (t) = 1 s
- Acceleration due to gravity (g) = -10 m/s² (negative because it acts downward)

### Step 2: Use the equation of motion to find the initial velocity (U)
We can use the second equation of motion:
\[ s = Ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ 10 = U(1) + \frac{1}{2}(-10)(1^2) \]
This simplifies to:
\[ 10 = U - 5 \]
Rearranging gives:
\[ U = 10 + 5 = 15 \, \text{m/s} \]

### Step 3: Use the initial velocity to find the final velocity (V)
Now that we have the initial velocity, we can use the first equation of motion to find the final velocity:
\[ V = U + at \]
Substituting the known values:
\[ V = 15 + (-10)(1) \]
This simplifies to:
\[ V = 15 - 10 = 5 \, \text{m/s} \]

### Final Answer
The velocity of the ball after 1 second at a height of 10 meters is **5 m/s**.

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