Position and Velocity of a Ball If a stationary ball is released at a height h_0
ID: 3808815 • Letter: P
Question
Position and Velocity of a Ball If a stationary ball is released at a height h_0 above the surface of the Earth with a vertical velocity v_0 the position and velocity of the ball as a function of time will be given by the equations h(t) = 1/2 gt^2 + v_0 t + h_0 v(t) = gt + v_0 where g is the acceleration due to gravity (-9.81 m/s^2), h is the height above the surface of the Earth (assuming no air friction), and v is the vertical component of velocity. Write a MATLAB program that prompts a user for the initial height of the ball in meters and the vertical velocity of the ball in meters per second, and plots the height and vertical velocity as a function of time. Be sure to include proper labels in your plots.Explanation / Answer
Here is the code for you:
initialHeight = input('Enter the initial height of the ball in meters: ');
verticalVelocity = input('Enter the vertical velocity of the ball in meters per second: ');
gravity = -9.81;
height(1) = initialHeight;
velocity(1) = verticalVelocity;
for i = 1 : 100
height(i) = -1/2 * gravity * i * i + verticalVelocity * sin(60) * i + initialHeight;
velocity(i) = gravity * i + verticalVelocity;
end
i = 1 : 100;
plot(i, height, 'x');
hold on;
plot(i, velocity, 'o');
xlabel('time');
ylabel('height');