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 0.4 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.

Answer 1

by taking the first derivative, we see that the maximum height is 36 ft and it reached at t = 1.5, as nicely prescribed by the h(t) equation for Earth. this means that all this would hold if the constants were modified.

mars gravity = 0.4 that of Earth. 16 comes from earth's gravity (32 ft/s2, but not important for this problem). so 0.4 * 16 = 6.4 = mars' gravity.

by plugging in the constants, the equation, with t max being (1.5 + 2.5) and height 59:

h(t) = -6.4(t - 4)^2 + 59