The formula  t=h√4
  represents the time t in seconds that it takes an object to fall from a height of h feet. If a rock falls from 125 feet, estimate how long it will take the rock to hit the ground. Estimate the square root to the nearest integer before dividing. Express your answer as a decimal.

 

about __ seconds



The formula \( t = h \sqrt{4} \) doesn't seem correct for modeling the time it takes an object to fall. In physics, the time \( t \) it takes for an object to fall from a height \( h \) under the influence of gravity is typically given by the formula:

\[
t = \sqrt{\frac{2h}{g}}
\]

where \( g \) is the acceleration due to gravity, approximately \( 32 \, \text{ft/s}^2 \) (for objects falling near Earth's surface), and \( h \) is the height in feet.

Given \( h = 125 \, \text{feet} \), we can use this formula to estimate the time \( t \).

### Step-by-step solution:

1. The formula becomes:
   \[
   t = \sqrt{\frac{2 \times 125}{32}}
   \]
2. Simplifying inside the square root:
   \[
   t = \sqrt{\frac{250}{32}} = \sqrt{7.8125}
   \]
3. Estimate \( \sqrt{7.8125} \) to the nearest integer:
   \[
   \sqrt{7.8125} \approx 3
   \]
4. So, the time it takes for the rock to fall is about \( 3 \) seconds.

Thus, it will take approximately **3 seconds** for the rock to hit the ground.

Would you like further details or have any questions?

Here are 5 related questions for exploration:
1. How does the height \( h \) affect the time \( t \) for an object to fall?
2. What is the significance of the constant \( g = 32 \, \text{ft/s}^2 \)?
3. How would the time change if the object was dropped from a height of 250 feet?
4. How does air resistance affect the time an object takes to fall?
5. Can we use the same formula for an object falling on the Moon?

**Tip:** Estimating square roots to the nearest integer is useful for quick approximations in physics problems.

The formula t = h√4 represents the time t in seconds that it takes an object to fall from a height of h feet. If a rock falls from 125 feet, estimate how long it will take the rock to hit the ground. Estimate the square root to the nearest integer before dividing. Express your answer as a decimal.

Estimate how long it takes for a rock to fall from 125 feet using the free-fall formula t = √(2h/g). Learn how to estimate square roots and simplify the calculation, with a step-by-step explanation of key kinematic concepts. Perfect for students in Grades 9-12 studying physics or kinematics.

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