Question

If a rock is thrown vertically upward from the surface of Mars with velocity ,

Answer 1

Step 1 :

(a)

The height of the rock after t seconds is .

Velocity at the surface of the Mars .

Velocity is the derivative of displacement function.

Differentiate h with respect to t.

Velocity of rock after t seconds .

Velocity of rock after 2 seconds:

Velocity of rock after 2 seconds is 7.56 m/s.

Step 2 :

(b)

The height is 25 m.

Height of the rock after t seconds .

Since roots of the quadratic function :

Roots of the quadratic function  :

First root:

Second root:

Step 3 :

Velocity at time .

At height 25 m the velocity of rock on its way up is .

Velocity at time .

At height 25 m the velocity of rock on its way down is .

Solution :

(a) Velocity of rock after 2 seconds is 7.56 m/s.

(b) The velocity of rock on its way up is .

     The velocity of rock on its way down is .