A ball of amass 500g is kicked in to the air at an angle of 45 degrees it reaches a height of 12m .then what is its kinetic energy and potential energy?
To calculate the kinetic energy and potential energy of the ball, we need to use the formulas associated with each form of energy.
1. Kinetic Energy (KE):
The formula for kinetic energy is KE = (1/2) * m * v^2, where m is the mass of the object and v is its velocity.
First, we need to find the object's velocity. To do this, we can use the vertical motion equations for an object thrown upwards:
h = (v_i^2)/(2g) [Equation 1],
where h is the maximum height reached, v_i is the initial vertical velocity, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Rearranging Equation 1, we can solve for v_i:
v_i = √(2gh) [Equation 2].
Substituting the given values into Equation 2:
h = 12 m
g = 9.8 m/s^2
v_i = √(2 * 9.8 * 12)
≈ √235.2
≈ 15.34 m/s (rounded to two decimal places)
Now, we can calculate the kinetic energy using the given mass and the calculated velocity:
KE = (1/2) * m * v^2
= (1/2) * 0.5 kg * (15.34 m/s)^2
= 0.5 * 0.5 * 235.2
≈ 58.8 Joules (rounded to one decimal place)
2. Potential Energy (PE):
The formula for potential energy is PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
Using the given values:
PE = 0.5 kg * 9.8 m/s^2 * 12 m
= 58.8 Joules
Therefore, the kinetic energy and potential energy of the ball are both approximately 58.8 Joules.