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Answer: minimum speed of launch must be 7.45m/s
Explanation:
Given the following:
Height or distance (s) = 2.83m
The final velocity(Vf) at maximum height = 0
Upward motion, acceleration due to gravity(g) us negative = -9.8m/s^2
From the 3rd equation of motion:
V^2 = u^2 - 2gs
Where V = final velocity
u = initial velocity
Therefore, u = Vi
u = √Vf^2 - 2gs
u = √0^2 - 2(-9.8)(2.83)
u = √0 + 55.468
u = √55.468
u = 7.4476 m/s
u = 7.45m/s
Answer:
T = 764.41 N
Explanation:
In this case the tension of the string is determined by the centripetal force. The formula to calculate the centripetal force is given by:
(1)
m: mass object = 2.3 kg
r: radius of the circular orbit = 0.034 m
v: tangential speed of the object
However, it is necessary to calculate the velocity v first. To find v you use the formula for the kinetic energy:

You have the value of the kinetic energy (13.0 J), then, you replace the values of K and m, and solve for v^2:

you replace this value of v in the equation (1). Also, you replace the values of r and m:

hence, the tension in the string must be T = Fc = 764.41 N
Explanation:
It is given that,
Force, 
Position vector, 
(a) The torque on the particle about the origin is given by :

(b) To find the angle between r and F use dot product formula as :

Hence, this is the required solution.