Science math HELP?

Question

Newton's law of cooling states that the rate at which an object cools varies directly as the difference between its temperature and the temperature of the surrounding air. At the moment a steel plate at 270 degrees Celsius is placed in air that is at 20 degrees Celsius, its rate of cooling is 50 degrees Celsius per minute. How fast is it cooling when the plate temperature is 100 degrees Celsius?

The centrifugal force acting on an object moving in a circle is directly proportional to the square of the speed of the object. If the force is 2240 newtons when the object is moving 8 m/s, what is the force when the object is moving at 12 m/s?

The speed of an object falling from rest is directly proportional to the square root of the distance the object has fallen. When an object has fallen 36 ft., its speed is 48 ft/s. How much farther must it fall before its speed is 80 ft/s?

Answer 1

Newton's law of cooling states that the rate at which an object cools varies directly as the difference between its temperature and the temperature of the surrounding air. At the moment a steel plate at 270 degrees Celsius is placed in air that is at 20 degrees Celsius, its rate of cooling is 50 degrees Celsius per minute. How fast is it cooling when the plate temperature is 100 degrees Celsius?

let:

td1 = 270 - 20 = 250

td2 = 100 - 20 = 80

cr1 = 50 [degr/min]

then:

cr2 = 80/250 * 50 = 8/25 * 50 = 400/25 = 16 [degr/min]

Answer: 16 [degr/min]

The speed of an object falling from rest is directly proportional to the square root of the distance the object has fallen. When an object has fallen 36 ft., its speed is 48 ft/s. How much farther must it fall before its speed is 80 ft/s?

let:

v1 = 48

v2 = 80

d1 = 36 [ft]

then:

d2 = (80/48)^2 * 36 = (5/3)^2 * 36 = 25/9 * 36 = 25 * 4 = 100 [ft]

Answer: speed will be 80 [ft/s] when object has fallen a 100 [ft]

The centrifugal force acting on an object moving in a circle is directly proportional to the square of the speed of the object. If the force is 2240 newtons when the object is moving 8 m/s, what is the force when the object is moving at 12 m/s?

let:

v1 = 8

v2 = 12

f1 = 2240 [N]

then:

f2 = (12/8)^2 * 2240 = (3/2)^2 * 2240 = 9/4 * 2240 = 9 * 560 = 5040 [N]

Answer: when object moves at 12 [m/s] force will be 5040 [N]

Good luck.