Ej is taking his little sister, ebony, on her first carousel ride. his mass is 75.0 kg, and her mass is 10.0 kg. they ride the same horse, and it is 11.0 meters from the center of the carousel. if their angular momentum is 14020 kg m2/s, what is their linear speed?

In this question we have given

mass of Ebony=75Kg

His sister mass=10kg

here total mass=mass of Ebony+his sister mass

m=75+10  

m=85kg

radius of circular path=11m

angular momentum=14020kgm^2/s

we know that,

angular momentum=interia*angular speed

angular momentum=I*w(1)

here, interia  I=mr^2  

and w=v/r (here v is the linear velocity and r is radius)

put  values of I and w in equation (1)

angular momentum=mr^2*v/r

angular momentum = mvr  

14020 = (75+10) x v x 11  

v = 14020/(85x11) = 14.99m/s

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft