Question

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds is given by H= 10t-1.86t^2. a). Find thevelocity of the rock after one second. b). Find the velocity of the rock when t=a. c). When will the rock hit the surface? d). With what velocity will the rock hit thesurface?

Answer 1

a) The height, h = 10t - 1.86t^2 The velocity can be represented as the derivative of the equation, h v = 10t - 1.86t^2 (d/dt) = 10 - (1.86*2)t ===>v(t) = 10 - 3.72t Thus, you can plug in t = 1, v(t) = 10 - 3.72(1)... v = 6.28m/s b) v(t) = 10 - 3.72(a) = 10-3.72a c) h = 10t - 1.86t^2 => 10t -1.86t^2 = 0 Factor - t(10-1.86t) Thus t = {0, 5.38s} at 5.38 s is when it hits the ground again d) v(t) = 10 - 3.72t plug in 5.38 Thus v = -10.08 m/s