Question

If a rock is thrown upward on the planet Mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H = 17t − 1.86t2.(a) Find the velocity of the rock after two seconds.9.6 Correct: Your answer is correct. m/s(b) Find the velocity of the rock when t = a. Correct: Your answer is correct. m/s(c) When will the rock hit the surface? (Round your answer to one decimal place.

Answer 1

(a) 9.6

(b)
`17 - 3.72a`

(c) 9.1 s

Step-by-step explanation:

Velocity is the time-derivative of position. From the question,

`H = 17t − 1.86t^2`

`v(t) = (d)/(dt)H = 17-3.72t`

(a) When
`t=2`

`v(t) = 17-3.72*2 = 17 - 7.44 = 9.56 = 9.6 \text { to 1 decimal place}`

(b) When
`t=a`

`v(a) = 17-3.72a`

(c) The rock will hit the surface when When
`H=0`.

`H = 17t − 1.86t^2 = 0`

`t(17 − 1.86t) = 0`

`t = 0` (This is when the rock was thrown)

or

`17 − 1.86t = 0`

`17 = 1.86t`

`t = (17)/(1.86) = 9.1398 = 9.1\text { to 1 decimal place}`