Question

"If a rock falls from a height of 25 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 25 -4.9x? (a) What is the height of the rock when x = 1.7 seconds? meter The height of the rock when x = 1.7 seconds is (Round to three decimal places as needed.) (b) When is the height of the rock 8 meters? seconds The height of the rock is 8 meters when x (Round to two decimal places as needed.) (c) When does the rock strike the ground? The rock strikes the ground when x seconds (Round to two decimal places as needed.)

Answer 1

The height of the rock at 1.7 seconds is approximately 10.839 meters. To find when the rock is at 8 meters or when it hits the ground, one must solve the equation for x, resulting in x corresponding to the times when the rock is at the desired heights.

Step-by-step explanation:

To solve for the height of the rock at a specific time when it is in free fall, we can use the equation H(x) = 25 - 4.9x². Let's address part (a) for the height when x = 1.7 seconds.

H(1.7) = 25 - 4.9(1.7)2 = 25 - 4.9(2.89) ≈ 25 - 14.161 = 10.839 meters.

For part (b), to find when the rock is at a height of 8 meters, we set H(x) = 8 and solve for x:

8 = 25 - 4.9x²
4.9x² = 25 - 8
4.9x² = 17
x² = 17 / 4.9
x ≈ √(3.469)

For part (c), the rock strikes the ground when H(x) = 0:

0 = 25 - 4.9x²
4.9x² = 25
x² = 25 / 4.9
x ≈ √(5.102)