To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function h(t) = -16t^2 + 78t + 5.
The t-value of the vertex is given by the formula t = -b/(2a), where a = -16 and b = 78.
Plugging in these values, we get t = -78/(2*-16) = 78/32 = 2.44 seconds.
To find the maximum height, we need to plug this value of t back into the function h(t) = -16t^2 + 78t + 5.
h(2.44) = -16(2.44)^2 + 78(2.44) + 5
h(2.44) = -16(5.9536) + 190.32 + 5
h(2.44) = -95.22 + 190.32 + 5
h(2.44) = 100.1 feet
Therefore, the T-shirt will take 2.44 seconds to reach its maximum height of 100.1 feet. The closest answer choice is C. 2.44 seconds; 100.06 feet.
12. During halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched with an initial upward velocity of 78 ft/s. The height of the T-shirt (h) in feet after t seconds is given by the function h = −16t^2 + 78t + 5. How long will it take the T-shirt to reach its maximum height? What is its maximum height?
A. 1.22 seconds; 76.35 feet
B. 2.44 seconds; 146.28 feet
C. 2.44 seconds; 100.06 feet
D. 2.44 seconds; 131 feet
1 answer
1 answer