Question

In: Physics

You have been employed by the local circus to plan their human cannonball performance. For this...

You have been employed by the local circus to plan their human cannonball performance. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a net below. The net is located 4 m lower than the muzzle of the cannon from which the Great Flyinski is launched. The cannon will shoot the Great Flyinski at an angle of 45 degrees above the horizontal and at a speed of 15 m/s. The ringmaster has asked you to determine a few things in order to make sure the show is both safe and entertaining.

a) The x-component of the human cannonball’s initial velocity and final are _____ m/s.

b) The y-component of the human cannonball’s initial velocity and final are _____ m/s.

c) Now, report the final speed of the human cannonball when he hits the net. The ringmaster will use this information to make sure she uses a strong enough net, as her circus has had problems with previous human cannonballs breaking through the bottom of the nets, and it has not been well-received.

d) How long is the human cannonball in the air? The ringmaster wants to make sure the human cannonball is in the air long enough to impress the audience.

Expert Solution

Let u be the initial velocity of this projectile. It can be resolved into 2 components . ucos (horizontally) and usin (vertically)

u=15m/s and =angle of projection=45

a)X compoent of initial velocity =ucos=15cos45=10.61m/s

b)Y compoent of initial velocity =usin=15sin45=10.61m/s

c)Horizontal velocity of projectile ucos is a constant throughout the motion (because no acceleration in X direction). But verical velocity usin changes as earth affects vertical motion

Consider vertical motion of this projectile and apply

=(xt)+a/2

=4m

=10.61

a=-9.8m/s2

t=time=?

=(xt)+a/2

4=10.61t-(9.8/2)=10.61t-4.9

4.9-10.61t+4=0

t={-(-10.61)±(}/(2x4.9)

t=1.679sec

Again

=+at

=final vertical velocity=?

=10.61-(9.8x1.679)=-5.845m/s

Final horizontal velocity =(itself)=10.61m/s

Resultant final velocity, v===12.11m/s

d) Time in which human cannonball in air=t=1.679second (solved in above part c)

genius_generous answered 1 year ago

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