Question

A rocket is launched vertically from the ground with an initial velocity of 64 ft/sec. A) Write a quadratic function h(t) that shows the height, in feet, of the rocket t seconds after it was launched. B) Graph h (t) on the coordinate plane. C) Use your graph from Part 3 (b) to determine the rocket's maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air. ( Answer options A,B,C) Please don't answer if you don't know how to) Will Mark Brainliest. ​

Answer 1

Answer:

a) h(t) = -16t² + 56t; b) the graph is attached; c) maximum height is 49 feet, it takes 1.75 seconds to reach the maximum, and it is in the air for 3.5 seconds.

Step-by-step explanation:

Equations for these situations are in the form

h(t) = -16t² + v₀t + h₀, where t is the tie in seconds, v₀ is the initial velocity and h₀ is the initial height. The initial height in this case is 0, since it is launched from the ground; and the initial velocity is 56.  This gives us the function

h(t) = -16t² + 56t

The graph is attached.

Using the graph, we can trace the function to the maximum.  The y-value of the maximum, or the maximum height, is 49 feet.  The x-value of the maximum, the time it takes, is 1.75 seconds.

The roots of this equation are at x = 0 and x = 3.5.  This means the rocket is in the air for 3.5-0 = 3.5 seconds.