Question

If a rock is thrown vertically upward from the surface of mars with velocity of 20 m/s, its height (in meters) after t seconds is h = 20t − 1.86t2. What is the velocity (in m/s) of the rock after 2 s?

Answer 1

The velocity of the rock after 2 seconds on Mars can be found by differentiating the height equation and substituting t with 2, resulting in a velocity of 12.56 m/s.

Step-by-step explanation:

The velocity of the rock after 2 seconds can be computed by taking the derivative of the height equation provided to obtain the velocity equation, and then substituting the time t with 2 seconds.

The height function provided is h = 20t - 1.86t2. The velocity v(t) of the rock at any time t is the derivative of the height function with respect to time t, which is v(t) = dh/dt = 20 - 2(1.86)t.

Substituting t = 2 s into the velocity equation gives v(2) = 20 - 2(1.86)(2) = 20 - 7.44 = 12.56 m/s. Therefore, the velocity of the rock after 2 seconds on Mars is 12.56 m/s.