A student wants to know how the motion of the rock would be different if it was thrown upward at 15m/s from a height of 100m above Earth’s surface. In a clear, coherent, paragraph-length response that may also contain figures and/or equations, explain how the motion of the rock on Earth will be different from its motion on Planet X in terms of its maximum height above the ground, the speed at which it reaches the ground, the time in which it is in free fall, and its acceleration due to gravity.

See explanation

Explanation:

Given:-

- The height from which rock is thrown, si = 100m

- The initial velocity, vi = 15 m/s

- Earth gravitational constant, g = 9.81 m/s^2

- Planet x gravitational constant = L

Find:-

explain how the motion of the rock on Earth will be different from its motion on Planet X in terms of its maximum height above the ground, the speed at which it reaches the ground, the time in which it is in free fall, and its acceleration due to gravity.

Solution:-

- Using third kinematic equation of motion in vertical direction. We have:

                           vf = vi + 2*a*(sf - si)

   vf : Final velocity

   a : Acceleration ( free fall )

   t : Time

   s : Distance travelled

For maximum height (sf) - vf = 0:

                            sf = vi / 2*a + si

    For earth , a = g

    For planet, x = L

For speed (vf) at ground - sf = 0 and vi = 0:

                            vf =  2*a*(-si)

    For earth , a = -g

    For planet, x = -L

- Using second kinematic equation of motion in vertical direction. We have:

                           sf = si + vi*t + 0.5*a*t^2

   sf : Final distance from ground

   a : Acceleration ( free fall )

   t : Time

   si : Initial distance from ground.

For time taken for entire journey (t) - (sf = 0):

                         0 = si + vi*t + 0.5*a*t^2

                         a*t^2 + 2*vi*t + 2*si = 0

                         t =  [ - ( 2*vi ) +/- √( 4vi^2 - 8*a*si ) ] / 2a    

For earth , a = g

For planet, x = L

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