Respuesta :
vertical speed u = v sinФ
Energy is conserved:
E = mgh = 1/2mu²
u = √(2gh)
v = √(2gh)/ sinФ
g = 9.81 m/s²
h = 3.5
Ф = 40°
Energy is conserved:
E = mgh = 1/2mu²
u = √(2gh)
v = √(2gh)/ sinФ
g = 9.81 m/s²
h = 3.5
Ф = 40°
The initial vertical speed required by the dolphin in order to reach the height of the hoop is 5.315 m/s.
Velocity
The velocity of an object can be defined as the rate of change in the position of the object with respect to time.
Given that the angle of inclination of the water is 40°. The height above the surface of the pool is 3.5 m. A dolphin is trying to jump through a hoop. In this case, the direction of the motion is vertical. Hence the initial vertical speed of the dolphin is given below.
[tex]u = v sin\theta[/tex]
Here u is the initial speed, v is the final speed and [tex]\theta[/tex] is the angle of inclination of water.
Also, the potential energy of the dolphin will be equivalent to its kinetic energy. Hence
PE = KE
[tex]mgh = \dfrac{1}{2} \times mv^2[/tex]
Where m is mass, g is gravitational acceleration and h is the height. We can write the above equation as,
[tex]2gh = v^2[/tex]
[tex]v = \sqrt{2gh} [/tex]
Substituting the value of v to calculate the initial vertical speed of the dolphin.
[tex]u = vsin \theta[/tex]
[tex]u = \sqrt{2gh} \times sin\theta[/tex]
[tex]u = \sqrt{2\times 9.8\times 3.5} \times sin 40^\circ [/tex]
[tex]u = 5.315 \;\rm m/s[/tex]
Hence we can conclude that the initial vertical speed required by the dolphin is 5.315 m/s.
To know more about the velocity, follow the link given below.
https://brainly.com/question/999862.
