Question

Using the conservation theorem of mechanical energy, perform:
A ball of 18,2 kg is fired from a cannon located on level ground, with initial speed of 181 m/s at an angle of 43 ° to the horizontal (neglecting the size of the weapon). Based on the above information

A. Applying the kinematic theory of the parabolic shot, determine the speed of the ball at the point of maximum height of the parabolic trajectory it describes.
B. Applying the conservation of mechanical energy, determine the value of the maximum height reached by the ball on the ground.
C. Applying again the conservation of mechanical energy, determine how quickly the ball returns to the ground level.
D. From the results obtained, establish two conclusions regarding the speed with which the cannon leaves and the speed with which it impacts the ground.

Answer 1

A. The vertical velocity component at highest point will be zero

velocity at higest point will be equal to initial horizontal component of velocity = 181*cos43 = 132.75 m/s

B. initial kinetic energy on ball due to vertiucal componet of velocity = 0.5*18.2*(181*sin43)² = 138664.47 J

let maximum height reached be h

18.2*9.8*h=138664.47

h=777.4 m

C. time taken to reach maximum height = 181*sin43/9.8=12.6 seconds

time taken to return to ground = 181*sin43/9.8=12.6 seconds

Total time taken = 12.6+12.6=25.2 seconds'

D.the speed at which the cannon leaves the ground and reached the ground will be equal