Aman stands on top of a 25 m tall cliff. the man throws a rock upwards at a 25 degree angle above the horizontal with an initial velocity of 7.2 m/s. what will be the vertical position of the rock at t = 2 seconds? what will be the horizontal position of the rock at that time?

a) vertical position at 2s: 50.68 m

b) horizontal position at 2s: 13.05 m

Explanation:

This situation is a good example of the projectile motion or parabolic motion, in which the travel of the rock has two components: x-component and y-component. Being the equations to find the position as follows:

x-component:

  (1)

Where:

is the rock's initial speed

is the angle at which the rock was thrown

is the time

y-component:

  (2)

Where:

 is the initial height of the rock

 is the height of the rock at 2 s

 is the acceleration due gravity

Knowing this, let's begin with the answers:

a) Vertical position at 2 s:

  (3)

  (4)

  (5)  This is the vertical position at 2 s

b) Horizontal position at 2 s:

   (5)

  (6)  This is the horizontal position at 2 s

Explanation:

It is given that,

Position of the man, h = 25 m

Initial velocity of the rock, u = 7.2 m/s

The rock is thrown upward at an angle of 25 degrees.

(a) Let y is the vertical position of the rock at t = 2 seconds. Using the equation of kinematics to find y as :

y = 11.48 meters

(b) Let x is the horizontal position of the rock at that time. It can be calculated as :

x = 13.05 meters

Hence, this is the required solution.