If an object is projected upward from ground level with an initial velocity of 96 ft per sec, then its height in feet after t seconds is given by s(t)equalsminus16tsquaredplus96t. Find the number of seconds it will take to reach its maximum height. What is this maximum height?

The object will reach its maximum height of 144 feet in 3 seconds.

Given information:

An object is projected upward from ground level with an initial velocity of 96 ft per sec.

The height in feet after t seconds is given by .

Now, it is required to find the time at which the object will reach its maximum height.

The object will reach maximum height when velocity of the object becomes zero.

So, the velocity of the object can be written as,

So, the time at maximum height can be calculated as,

So, after 3 seconds the object will reach its maximum height.

Now, the maximum height of the object will be,

Therefore, the object will reach its maximum height of 144 feet in 3 seconds.

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Number of seconds to reach maximum height = 3 seconds

Maximum height = 144 ft

Step-by-step explanation:

We are given that;

s(t) = -16t² + 96t

Now, s(t) is a function whose graph is an upside-down parabola, so the maximum s value occurs at the vertex.

Thus, the applicable formula for coordinate of vertex is t = -b/(2a) where a is the coefficient -16 and b is 96

Thus,t = -96/(2 x - 16)

t = 96/32

t = 3

Thus maximum height will be at 3 seconds.

Thus;

Max height = s(3) = -16(3)² + 96(3)

Max height = -144 + 288 = 144 ft

Step-by-step explanation:

dy/dt=(y+1)(2√t)

separate the variables and integrating