A cricket ball hits the ground with kinetic energy K at an angle 30* with the vertical. What will be its kinetic energy at the highest point?
To determine the kinetic energy of the cricket ball at the highest point, we need to understand how energy changes during the ball's trajectory. Here's how you can find the solution step by step:
Step 1: Analyze the initial kinetic energy
The initial kinetic energy K of the ball hitting the ground is given. However, we can separate the components of this kinetic energy in the horizontal and vertical directions. Since the ball strikes the ground at an angle of 30 degrees with the vertical, we can break down the initial kinetic energy into horizontal and vertical components.
Step 2: Determine the vertical and horizontal components of kinetic energy
The vertical component of the initial kinetic energy can be found using trigonometry. Recall that the sine function relates the side opposite the angle to the hypotenuse of a right triangle. In this case, the vertical component (Kv) is given by:
Kv = K * sin(30°)
Similarly, the horizontal component (Kh) of the initial kinetic energy can be determined using the cosine function:
Kh = K * cos(30°)
Step 3: Analyze the highest point of the ball's trajectory
At the highest point of the ball's trajectory, its vertical velocity will be zero. This means that it will have no vertical kinetic energy at this point.
Step 4: Find the final kinetic energy at the highest point
Since the vertical kinetic energy is zero at the highest point, the total kinetic energy at this point will be equal to the horizontal kinetic energy. Therefore, the kinetic energy at the highest point (K') can be expressed as:
K' = Kh
Substituting the previously calculated value of Kh, we have:
K' = K * cos(30°)
So, the kinetic energy of the cricket ball at the highest point is K times the cosine of 30 degrees.