Question

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/s2 due to Earth's gravity. The gravity on Mars is only 0.38 times that on Earth. If the same baseball were thrown on Mars, it would reach a maximum height 59 feet higher and 2.5 seconds later than on Earth. Write a height function for the baseball thrown on Mars.

Answer 1

\(\large\color{black}{ \displaystyle h(t) = -16(t - 1.5)^2 + 36 }\)

The acceleration due to gravity on earth is: \(-16ft/s^2\)
(2nd derivative of the function)

and thus on Mars acceleration would be 6.08

Answer 2

\(\large\color{black}{ \displaystyle M(t) = -6.08(t - ?)^2 + ? }\)

Answer 3

Maximum height on earth is 36, thus on Mars is?

Answer 4

I mean y = -0.38(t - 4)2 + 95

Answer 5

\(\large\color{black}{ \displaystyle Mars(t) = (-16\color{red}{\times 0.38})(t - 1.5\color{red}{-2.5})^2 + 36 \color{red}{+59} }\)

\(\large\color{black}{ \displaystyle Mars(t) = (-6.08)(t - 4)^2 + 95 }\)

Answer 6

So just the front coefficient you didn't get correctly, but the rest - jood job!