A softball pitcher throws a softball to a catcher behind home plate. The softball is 3 feet above the ground when it leaves the pitcher’s hand at a velocity of 50 feet per second. If the softball’s acceleration is negative 16 the fraction with numerator ft and denominator s squared , which quadratic equation models the situation correctly? h of t is equal to A t squared plus v t plus h sub 0
Answer
A
3 is equal to negative 16 t squared plus 50 t plus h sub 0
B
h of t is equal to 50 t squared minus 16 t plus 3
C
h of t is equal to negative 16 t squared plus 50 t plus 3
D
3 is equal to 50 t squared minus 16 t plus h sub 0
Explanation
Use the height model h(t) = A t² + v t + h₀. The initial height is h₀ = 3 feet and the initial velocity is v = 50 feet per second. Since the given acceleration is −16 feet per second squared, the quadratic coefficient is −16, so h(t) = −16t² + 50t + 3, which is choice B.
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