"a 4 kg ball is thrown at an angle of 40 degrees above the horizon from the top of a 150 m cliff. how far from the base of the cliff does it land of the initial velocity is 30 m/s

180.102m

Explanation:

This situation is a good example of the projectile motion or parabolic motion, in which the travel of the ball after it is thrown from the top of the cliff has two components: x-component and y-component. Being their main equations as follows:

x-component:

  (1)

Where:

is the ball's initial speed

is the angle above the horizon

is the time since the ball is thrown until it hits the ground

y-component:

  (2)

Where:

 is the initial height of the ball

 is the final height of the ball (when it finally hits the ground)

 is the acceleration due gravity

Knowing this, let's begin with the calculations:

Firstly, we have to find the time the ball elapsed traveling. So, we will use equation (2) with the conditions given above:

(3)  

Isolating from (3):  

(4)  

(5)  

Substituting (5) in (1):  

  (6)  

Finally:

  (7)