g How many rpm would a 25 m diameter Ferris wheel need to travel if a 75 kg person were to experience an effective weight of 810 N at the lower-most point of the ride

2.52 rpm

Explanation:

given that

diameter of the wheel, d = 25 m

Mass of the person, m = 75 kg

Weight experienced, N = 810 N

Since diameter is 25, radius then is 25/2 = 12.5 m

We all know that,

v = rw

Also, the passengers weight is equal to the centripetal acceleration, and thus

mg = mv²/r

Substitute for v, we have

mg = m/r * (rw)²

mg = mr²w²/r

g = rw²

If we make w the subject of formula, we have

w² = g/r

w = √(g/r)

mg = 810

75 * g = 810

g = 810 / 75

g = 1.08 m/s²

w = √(g/r)

w = √(1.08 / 12.5)

w = √0.0864

w = 0.294 rad/s

Since the question asked us in rpm, we convert to rpm

0.294 * (60 / 2π)

2.52 revolution per minute.

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

after 28s,

m/s

which i would round to 150 m/s as my final answer

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min