Question

If a rock is thrown upward on the planet Mars with a velocity of 19 m/s, its height (in meters) after t seconds is given by H = 19t − 1.86t2.

(a) Find the velocity of the rock after one second. m/s
(b) Find the velocity of the rock when t = a. m/s
(c) When will the rock hit the surface? (Round your answer to one decimal place.) t = s
(d) With what velocity will the rock hit the surface? m/s

Answer 1

Below

Explanation:

A) The derivative of the position function is the velocity function

derivative = 19 - 3.72 t at t = 1 this = 15.28 m/s

B) unclear: 19 - 3.72a

C) H= 0 when at surface

0 = 19t - 1.86 t^2

Quadratic Formula shows t = 10.2 s

D ) it will come down at the same speed it went up (but opposite direction) = -19 m/s