**Newtons Law of Cooling Problem:**

**(1-3) **Assume that a body cools according to Newton’s law dѲ/dt = -kѲ where t is the time and Ѳ is the temperature T of the body and that of the surrounding air.

**1. **Find the temperature T at time t of a boiler of water cooling in air at 0 ⁰C if the water is initially boiling at 100 ⁰C and the temperature dropped by 10 ⁰C during the first 20 minutes.

A. T=100(0.9)t/20

B. T=100(0.8)t/20

C. T=80(0.9)t/20

D. T=80(0.8)t/20

**2. **Find the time for the temperature of the water to drop from 90 to 80 ⁰C.

A. 20 min

B. 42.4 min

C. 22.4 min

D. 62.4 min

**3. **Find the temperature of the water after 90 minutes.

A. 45.4 ⁰C

B. 50.9 ⁰C

C. 57.5 ⁰C

D. 62.2 ⁰C

**TRIGONOMETRY PROBLEM**

**4.** A uniform ladder 35 m long rests against a friction less wall with its lower end 21 m from the wall. The ladder weighs 80 N. The coefficient of static friction between the foot of the ladder and the ground is 0.40. A man weighing 150 N starts up the ladder. How far up the ladder can he climb before the ladder starts to slip?

A. 19.3 m

B. 22.1 m

C. 24.8 m

D. 26.1 m

**5. **A 12 foot ladder weighing 40 pounds is leaning on a wall such that it makes an angle of 60⁰ with the floor. When a 180 pound-man reaches a point 8 feet from the lower end of the ladder, the ladder is just about to slip. Determine the friction coefficient between the ladder and the floor. The coefficient of friction between the ladder and the walls is 0.20.

A. 0.20

B. 0.25

C. 0.30

D. 0.35

**IMPORTANT NOTE: **These are just practice problems I randomly collected solely for review purposes only. This should not be substituted to textbooks. Please read and study your textbooks well.

Answers are found in the next page

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