Cant figure out how to apply into formulas. Please show step by step and also wr

Question

Cant figure out how to apply into formulas. Please show step by step and also write the formulas for question before plugging in the numbers.

A)       A 25 g stone is tied to the end of a string and moves in a horizontal, circular path. The radius of the circle is 1.5 m.How long will it take the stone to make 30 complete revolutions if the tension in the string is 3.0 N

C)      A car drives straight off the edge of a cliff that is 45 m high. The police at the scene of the accident note that the point of impact is 125 m from the base of the cliff. How fast was the car traveling when it went over the cliff?

Explanation / Answer

A) Given T = 3N

Tension is responsible for centripital force.

=> Centripital frce = mw^2*R = T

=> w = Sqrt(T/mR) = Sqrt(3/(0.025*1.5) = 8.94 rad/s

1 rev = 2pi radian angle

=> 30 rev = 60pi radian angle

As it rotates 8.94 radian in 1 sec

=> it rotates 1 radian in (1/8.94) sec

=> 60pi radians in (60pi*(1/8.94)) sec = 21.1 sec

B)a = (v - u)/t = {(52.7 - 24.4)km/h}/(8.5s) = 3.33(km/h*s) = 3.33(1000m/3600s*s) = 0.925 m/s^2

Now a = alpha *R

=> R = (0.925/4.932) = 0.188 m

C)Horizontal projectile question:

Range = v*t

Vertical height = 0.5*gt^2

Given : 0.5gt^2 = 45

=> t = 3.03 s

=> 125 = vt = v*3.03

=> v = 41.25 m/s

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