Trained dolphins are capable of a vertical leap of 7.0m straight up from the surface of the water-an impressive feat. suppose you could train a dolphin to launch itself out of the water at this same speed but at an angle.
what maximum horizontal range could the dolphin achieve?

14 m

Explanation:

This situation is related to parabolic motion, in which the motion of the dolphins has two components: x-component and y-component. Being their main equations as follows:  

x-component:  

  (1)  

(2)  

Where:  

is the dolphin's initial speed  

is the angle

is the time since the dolphin jumps until it goes to the water surface again

is the horizontal component of the initial velocity

y-component:  

(3)

  (4)  

  (5)  

Where:  

is the maximum height the dolphin can reach (when )  

is the velocity of the dolphin at its maximum height

is the acceleration due gravity

is the vertical component of the initial velocity

Let's begin with (3) when (straight up leap):

(6)

Finding :

(7)

Isolating from (4):

  (8)  

Substituting (7) and (8) in (1):

(9)  

(10)  

is maximum when . This means:

Hence, the maximum horizontal range the dolphin could achieve is when :

(10)  

Finally:

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