Questions: Solve the problem. If a rock falls from a height of 20 meters on Earth, the height H (in meters) after x seconds is approximately H(x)=20-4.9 x^2 When does the rock strike the ground? Round to the nearest hundredth, if necessary.

Solve the problem.

If a rock falls from a height of 20 meters on Earth, the height H (in meters) after x seconds is approximately

H(x)=20-4.9 x^2

When does the rock strike the ground? Round to the nearest hundredth, if necessary.

Transcript text: Solve the problem. If a rock falls from a height of 20 meters on Earth, the height H (in meters) after $\times$ seconds is approximately \[ H(x)=20-4.9 x^{2} \] When does the rock strike the ground? Round to the nearest hundredth, if necessary.

Solution

Solution Steps

Step 1: Set the height equation to zero

To find when the rock strikes the ground, set the height $ H(x) $ to zero: \[ 0 = 20 - 4.9x^2 \]

Step 2: Solve for $ x^2 $

Rearrange the equation to solve for $ x^2 $: \[ 4.9x^2 = 20 \]

Step 3: Solve for $ x $

Divide both sides by 4.9: \[ x^2 = \frac{20}{4.9} \] \[ x^2 \approx 4.08 \] Take the square root of both sides: \[ x \approx \sqrt{4.08} \] \[ x \approx 2.02 \]

The rock strikes the ground at approximately $ x = 2.02 $ seconds.