The height \( h \) in feet of a baseball on Earth after \( t \) seconds can be modeled by the function \( h(t) = -16(t – 1.5)^2 + 36 \), where \(-16\) is a constant in ft/s\(^2\) due to Earth's gravity. The gravity on Mars is only 0.4 times that on Earth. If the same baseball were thrown on Mars, it would reach its maximum height 59 feet higher and 2.5 seconds later than it did on Earth. Write a height function for the baseball thrown on Mars.
A) \( y = -0.4(t – 4)^2 + 95 \)
B) \( y = -0.4(t – 2.5)^2 + 59 \)
C) \( y = -6.4(t – 4)^2 + 95 \)
D) \( y = -6.4(t – 2.5)^2 + 59 \)
Answer (2)
y = (-16*0.4)(t - 2.5-1.5)^2 + 36 + 59 y = 6.4(t - 4)^2 + 95
The height function for the baseball thrown on Mars is given by y ( t ) = − 6.4 ( t − 4 ) 2 + 95 . This function reflects the maximum height of 95 feet reached at 4 seconds. Therefore, the correct option is C.
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