The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 22.5 m/s is h = 2 + 22.5t − 4.9t2 after t seconds. (Round your answers to two decimal places.)(a) Find the velocity after 2 s and after 4 s. v(2) = m/sv(4) = m/s(b) When does the projectile reach its maximum height?s(c) What is the maximum height?m(d) When does it hit the ground?s(e) With what velocity does it hit the ground?m/s

a) , b) , c) , d) , e) , f)

Step-by-step explanation:

The velocity function can be derived by the differentiating the height function:

Velocities after 2 and 4 seconds are, respectively:

a)

b)

The maximum height is reached when velocity is zero. Then:

c)

The maximum height is:

d)

The time required to hit the ground is:

Roots of the second-order polynomial are:

Only the first root is physically reasonable.

e)

The velocity when the projectile hits the ground is:

f)

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