A rock is projected directly upward from ground level with an initial velocity of 90 feet per second. Give the function that describes the height of the rock in terms of time t.

Step-by-step explanation:

From the fourth law of motion

h = ut + 0.5gt^2

h = 90t + 0.5 (10) t^2

Converting 90 frets/s into m/s

h = 27.43t + 5t^2

Step-by-step explanation:

The initial velocity, u of the obect when it was projected vertically is 90 feet per second

The acceleration of the object is 32.17405 ft/s2 which is approximately 32.2ft/s2. This is same as acceleration due to gravity.

Since the object is moving upwards, it is moving in opposite direction to the gravitational force. Therefore,

acceleration of the object, g is negative.

g = - 32.2ft/s2

u = 90 feet per second

H = the height of the object in feets

t = time in seconds

Applying newtons law of motion

H = ut + gt^2/2

H = 90t + (-32.2*t^2) / 2

H = 90t - 16.1t^2

H = - 16.1t^2 + 90t^2

The function is

f (t) = - 16.1t^2 + 90t^2