Explanation:
To calculate the potential energy of the ball at its highest point, we first need to find the gravitational potential energy of the ball. Gravitational potential energy is given by the equation:
PE = mgh
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2 on the surface of the earth), and h is the height of the ball above the ground.
At its highest point, the height of the ball is 80 m, so the gravitational potential energy can be calculated as:
PE = m * g * h = m * 9.8 * 80
where m is the mass of the ball.
Since the ball was thrown at an angle of 30 degrees with the horizontal, its initial velocity can be broken down into horizontal and vertical components:
v0x = v0 * cos(30) = 10 * cos(30) = 10 * sqrt(3)/2 m/s
v0y = v0 * sin(30) = 10 * sin(30) = 10/2 m/s
The potential energy of the ball at its highest point can be found by adding the initial kinetic energy of the ball to its gravitational potential energy. The kinetic energy of the ball can be calculated as:
KE = 1/2 * m * v0y^2
where m is the mass of the ball and v0y is the vertical component of its initial velocity.
The total potential energy of the ball at its highest point is given by:
PE = KE + mgh = 1/2 * m * v0y^2 + m * g * h
Substituting in the given values, we find:
PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80
Note: The mass of the ball (m) is not given, so the answer is given in terms of m.