A particle is moving along a projectile path at an initial height of 96 feet with an initial speed of 16 feet per second. This can be represented by the function H(t) = −16t2 + 16t + 96. What is the maximum height of the particle?
100 feet
96 feet
60 feet
56 feet
1 answer
The maximum height occurs at the vertex of the parabolic function, which is given by t=-b/2a. In this case, a=-16 and b=16, so t=-16/(2*(-16))=0.5 seconds. Plugging this time into the function, we get H(0.5)=-16(0.5)^2 + 16(0.5) + 96 = 100 feet. Therefore, the maximum height of the particle is 100 feet. Answer: \boxed{100\text{ feet}}.
1 answer