Sure, let's solve this step by step.

1. **Identify the given values:**
- Initial height (h) = $ h $
- Acceleration due to gravity (g) = $ g $
- Initial velocity (u) = 0 (since the ball is dropped)

2. **Use the kinematic equation for motion under constant acceleration:**
$$
h = ut + \frac{1}{2}gt^2
$$

3. **Substitute the known values into the equation:**
$$
h = 0 \cdot t + \frac{1}{2}gt^2
$$
Simplifying, we get:
$$
h = \frac{1}{2}gt^2
$$

4. **Solve for time (t):**
$$
t^2 = \frac{2h}{g}
$$
$$
t = \sqrt{\frac{2h}{g}}
$$

So, the time it will take for the ball to reach the ground is:
$$
t = \sqrt{\frac{2h}{g}}
$$

Question

Sure, let's solve this step by step.

1. **Identify the given values:**
   - Initial height (h) = $ h $
   - Acceleration due to gravity (g) = $ g $
   - Initial velocity (u) = 0 (since the ball is dropped)

2. **Use the kinematic equation for motion under constant acceleration:**
   $$
   h = ut + \frac{1}{2}gt^2
   $$

3. **Substitute the known values into the equation:**
   $$
   h = 0 \cdot t + \frac{1}{2}gt^2
   $$
   Simplifying, we get:
   $$
   h = \frac{1}{2}gt^2
   $$

4. **Solve for time (t):**
   $$
   t^2 = \frac{2h}{g}
   $$
   $$
   t = \sqrt{\frac{2h}{g}}
   $$

So, the time it will take for the ball to reach the ground is:
$$
t = \sqrt{\frac{2h}{g}}
$$

Knowee AI · Accepted Answer

Sure, let's solve this step by step.

1. **Identify the given values:**
   - Initial height (h) = $ h $
   - Acceleration due to gravity (g) = $ g $
   - Initial velocity (u) = 0 (since the ball is dropped)

2. **Use the kinematic equation for motion under constant acceleration:**
   $$
   h = ut + \frac{1}{2}gt^2
   $$

3. **Substitute the known values into the equation:**
   $$
   h = 0 \cdot t + \frac{1}{2}gt^2
   $$
   Simplifying, we get:
   $$
   h = \frac{1}{2}gt^2
   $$

4. **Solve for time (t):**
   $$
   t^2 = \frac{2h}{g}
   $$
   $$
   t = \sqrt{\frac{2h}{g}}
   $$

So, the time it will take for the ball to reach the ground is:
$$
t = \sqrt{\frac{2h}{g}}
$$

A student drops a ball from a height of . The acceleration of the ball due to gravity is .How long will it take the ball to reach the ground?

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