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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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: place value, base value, decimal expansion, whole number, natural number, division, multiplication, subtraction, solve the equation, solution, linear equation, line, decimal.