Problema Solution
A fireworks shell is shot straight up with an initial velocity of 130 feet per second. Its height s after t seconds is given by the equation s = 130t - 16t2. If the shell is designed to explode when it reaches its maximum height, how long after being fired, and at what height, will the fireworks appear in the sky?
Answer provided by our tutors
s = 130t - 16t^2
we need to find the maximum height and the value for t that height is reached
the parabolic function y = ax^2 +bx + c has a maximum if a<0 and it is calculated by the formula y max = c - (b^2)/(4a)
in our case s = 130t - 16t^2 we have -16<0 the function has a maximum h max
h max = 0 - (130^2)/(4*(-16))
h max = 264.0625 ft
the fireworks will appear at 264.0625 ft height
lets find the value for t for which s = -(130^2)/(4*(-16))
130t - 16t^2 = 264.0625
by solving we find
t = 4.0625 s
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the fireworks will appear 4.0625 seconds after being fired.