A body is projected at an angle 30 degree to the horizontal with kintic energy E.The kinetic energy at the topmost point is?

To find the kinetic energy at the topmost point of a body projected at an angle of 30 degrees to the horizontal, we can break down the problem into different components.

Step 1: Find the initial velocity

The kinetic energy of the body is given by the formula:
E = (1/2)mv^2

where E is the kinetic energy, m is the mass of the body, and v is the velocity of the body.

Since the body is projected at an angle of 30 degrees to the horizontal, we can break down the initial velocity into horizontal and vertical components. The horizontal component can be found using the formula:
Vx = v * cosθ

where Vx is the horizontal component of the velocity and θ is the angle of projection.

In this case, the angle of projection is given as 30 degrees, so we have:
Vx = v * cos30°

Step 2: Find the vertical component of the initial velocity

The vertical component can be found using the formula:
Vy = v * sinθ

where Vy is the vertical component of the velocity and θ is the angle of projection.

In this case, the angle of projection is given as 30 degrees, so we have:
Vy = v * sin30°

Step 3: Find the maximum height

The body reaches its highest point when its vertical velocity component becomes zero. At this point, all the initial kinetic energy is converted into potential energy.

Using the equation of motion for vertical motion which states that Vy^2 = Uy^2 + 2gh, where Uy is the vertical component of the initial velocity, g is the acceleration due to gravity, and h is the maximum height reached.

We can rearrange the equation to solve for h:
h = (Vy^2) / (2g)

In this case, Vy is the vertical component of the initial velocity and g is the acceleration due to gravity.

Step 4: Calculate the kinetic energy at the topmost point

The kinetic energy at the topmost point is zero since all the initial kinetic energy is converted into potential energy.

E/2

E=m•vₒ²/2

vₒ=sqrt(2•E/m).
At the top point v(y) = 0.
The velocity of the body =v(x)=v(ox)
v=v(0x) =vₒ•cosα.
E(kin) = mv²/2=
= m(vₒ•cosα) ²/2=
= m• (2•E/m) •cos²α /2=
=2•E• cos²α/2= E• cos²α=0.75E