Aprojectile is launched upward with a velocity of 288 feet per second from the top of a 65 foot structure . what is the maximum height attained by the projectile ?

The maximum height attained by the projectile is 412.94 meters = 1359.79 feet.

Step-by-step explanation:

The height formula has the following formula:

In which is the initial height, is the initial speed and g = 9.8 m/s² is the gravity.

In this problem, we have that:

We are working with the gravity in meters, so we must convert the feet measures to meters.

Each feet has 0.3048 meters.

So 288 feet per second = 87.78 meters per second.

65 foot = 19.81 meters.

This means that:

So

The maximum height is attained at the moment of time in which the velocity is 0. The velocity is the derivative of the height. So:

The maximum height is attained at 8.96s. This height is

The maximum height attained by the projectile is 412.94 meters = 1359.79 feet.

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute:

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.