1 answer:
Answer:
- 2 seconds
- 72 feet
Step-by-step explanation:
The usual equation used for the vertical component of ballistic motion is ...
h(t) = -16t² +v₀t +h₀
where v₀ is the initial upward velocity, and h₀ is the initial height. Units of distance are feet, and units of time are seconds.
Your problem statement gives ...
v₀ = 64 ft/s
h₀ = 8 ft
so the equation of height is ...
h(t) = -16t² +64t +8
__
For quadratic ax² +bx +c, the axis of symmetry is x=-b/(2a). Then the axis of symmetry of the height equation is ...
t = -64/(2(-16)) = 2
The object will reach its maximum height after 2 seconds.
The height at that time will be ...
h(2) = -16(2²) +64(2) +8 = 72
The maximum height will be 72 feet.
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Let n be the total number of rows and there are x seats is the 1st row where x is an odd natural number.
As each row must have 2 more seats than the one before it, so
Number of seats in 2nd row = x+2
Number of seats in 3rd row = x+2+2=x+2x2
Number of seats in 4th row = x+2+2+=x+2x3
Similarly, the number of seats in (n-1)th row =x+2x(n-1)
the number of seats in n^{th} row, i.e last row =x+2x n.
As the front row must have one-quarter of the total seats in the back 2 rows combined, so
So, the number of seats in the 1st row, x, and the total number of seats, n, must satisfy the equation (i).
For
So, for n=3 rows
The number of seats in the 1st row, x= 2x3-3=3.
The number of seats in the 2nd row, = 3+2=5 as in subsequent rows, there will be 2 more seats.
and the number of seats in the 3rd row (last row)=5+2=7.
n can have any integral values satisfying .