A cannon launches a ball with the initial speed of 210 m/s at a 70 degree angle.
1. How high will the cannonball go?
2. If the cannonball has a mass of 25kg how much work does it take to launch the cannonball to that height?
Vo = 210m/s[70o]
Xo = 210*cos70 = 71.82 m/s.
Yo = 210*sin70 = 197.3 m/s.
1. h = (Y^2-Yo^2)/2g=(0-197.3^2)/-19.6 =
1986 m.
To answer the first question, we can use the equations of projectile motion. The height reached by the cannonball can be found using the following formula:
h = (v^2 * sin^2(theta)) / (2 * g)
Where:
- h is the height
- v is the initial velocity (210 m/s)
- theta is the launch angle (70 degrees)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Let's calculate the height:
h = (210^2 * sin^2(70)) / (2 * 9.8)
h ≈ 759.37 meters
Therefore, the cannonball will reach a height of approximately 759.37 meters.
To answer the second question, we need to calculate the work done to launch the cannonball to that height. Work is defined as the product of force and displacement in the direction of the force. In this case, we'll use gravitational potential energy as a measure of work done. The work done to raise an object to a certain height is given by:
Work = m * g * h
Where:
- Work is the work done (to be calculated)
- m is the mass of the cannonball (25 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height reached by the cannonball (759.37 meters)
Let's calculate the work:
Work = 25 * 9.8 * 759.37
Work ≈ 185,543.45 Joules
Therefore, it takes approximately 185,543.45 Joules of work to launch the cannonball to that height.