Questions: Assuming the acceleration due to gravity is 10 m / s^2, how long will it take for a ball be falling 32 m / s?

Assuming the acceleration due to gravity is 10 m / s^2, how long will it take for a ball be falling 32 m / s?
Transcript text: Assuming the acceleration due to gravity is $10 \mathrm{~m} / \mathrm{s}^{2}$, how long will it take for a ball be falling $32 \mathrm{~m} / \mathrm{s}$ ?
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Solution

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Solution Steps

Step 1: Identify the Given Values

We are given the acceleration due to gravity \( g = 10 \, \text{m/s}^2 \) and the final velocity \( v = 32 \, \text{m/s} \). We need to find the time \( t \) it takes for the ball to reach this velocity from rest.

Step 2: Use the Kinematic Equation

The kinematic equation that relates acceleration, initial velocity, final velocity, and time is: \[ v = u + at \] where:

  • \( v \) is the final velocity,
  • \( u \) is the initial velocity,
  • \( a \) is the acceleration,
  • \( t \) is the time.

Since the ball starts from rest, the initial velocity \( u = 0 \).

Step 3: Solve for Time

Substitute the known values into the equation: \[ 32 = 0 + 10t \] \[ 32 = 10t \] Solve for \( t \): \[ t = \frac{32}{10} = 3.2 \, \text{s} \]

Final Answer

The time it takes for the ball to reach a velocity of \( 32 \, \text{m/s} \) is \(\boxed{3.2 \, \text{s}}\).

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