Question

A model rocket is launched with an initial upward velocity of 45 m/s. The rocket's height h (in meters) after t seconds is given by the following: h=−4.9t2+45t+512. Find all values of t for which the rocket's height is 20 meters.

Answer 1

To find all the values of t when the rocket's height is 20 meters, we can set the height equation equal to 20 and solve for t. The values of t are 4 seconds and approximately -24.9 seconds. Therefore, the rocket's height is 20 meters at t = 4 seconds.

Step-by-step explanation:

To find the values of t when the rocket's height is 20 meters, we can set the height equation, h = -4.9t^2 + 45t + 512, equal to 20 and solve for t. Here's how:

1. Substitute 20 for h in the equation:

   20 = -4.9t^2 + 45t + 512

2. Rearrange the equation:

   0 = -4.9t^2 + 45t + 492

3. Solve for t. You can do this by factoring, using the quadratic formula, or graphing. By factoring, we can rewrite the equation as:

   0 = (t - 4)(-4.9t - 123)

4. Set each factor equal to 0 and solve for t:

   t - 4 = 0 or -4.9t - 123 = 0

5. Solve each equation:

   t = 4 seconds or t ≈ -24.9 seconds (approximately)

Therefore, the rocket's height is 20 meters at t = 4 seconds.