MAJ’s height as a function of time is:
h(t) = -16t2 + At + B
A = 13 + sum of birthdate days
B = 25 + product of 2 birthdate months
Now, Birthdates are:
Therefore values of A and B will be:
A = 13 + 15 + 16 = 44
B = 25 + 6x8 = 73
Now, the given function of height of MAJ becomes:
h(t) = -16t2 + 44t + 73
1. How high above the ground is the tower?
Differentiate H (t) with respect to time to get speed in vertical direction.
dh/dt = v
v = d/dt (-16t2+44t+73)
v = -32t + 44
This equation is giving us the velocity of MAJ during its flight at any time t.
At the top of trajectory, velocity is zero.
v = 0 at top
v = -32t + 44 + 0
32t = 44
t = 44/32
t = 1.375s
This is the time for max height.
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.
-16t2 + 44t + 73 + 0
Using quadratic formula:
Two values of time will be:
t = -1.17s,3.92s
Here, time can’t be negative.
t = -1.17s (not possible)
Therefore, the time when MAJ hit the ground will be:
t = 3.92s
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