__Assignment__

** Given Data**:

MAJ’s height as a function of time is:

h(t) = -16t^{2} + At + B

Here:

A = 13 + sum of birthdate days

And:

B = 25 + product of 2 birthdate months

Now, Birthdates are:

06/15,08/16

Therefore values of A and B will be:

A = 13 + 15 + 16 = 44

And:

B = 25 + 6x8 = 73

Now, the given function of height of MAJ becomes:

h(t) = -16t^{2} + 44t + 73

** Questions**:

**1. How high above the ground is the tower**?

** Step i**:

Differentiate H (t) with respect to time to get speed in vertical direction.

dh/dt = v

v = d/dt (-16t^{2}+44t+73)

v = -32t + 44

This equation is giving us the velocity of MAJ during its flight at any time t.

** Step ii**:

At the top of trajectory, velocity is zero.

Thus:

v = 0 at top

v = -32t + 44 + 0

32t = 44

t = 44/32

t = 1.375s

This is the time for max height.

** Step iii**:

Put time for max. Height in H (t):

h = -16(1.375)^{2} + 44(1.375) + 73

h = -30.25 + 60.5 + 73

h = 103.25m

This is the maximum height for the MAJ’s trajectory.

Thus, it’s height of the tower.

**2. When does MAJ hit the ground**?

For MAJ at ground level:

h(t) + 0

Because, at ground level the vertical displacement is zero.

Thus:

-16t^{2} + 44t + 73 + 0

Using quadratic formula:

Two values of time will be:

t = -1.17s,3.92s

Here, time can’t be negative.

Thus,

t = -1.17s (not possible)

Therefore, the time when MAJ hit the ground will be:

t = 3.92s

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