How to solve problems involving Differential Calculus
Tutorial on how to solve problems involving Differential Calculus
Problems inside this video:
Problem 1: A light is at the top of a pole 80 feet high. A ball is dropped from the same height (80 ft.) from a point 20 feet from the light. Assuming that the ball falls according to the law s = 16t2, how fast is the shadow of the ball moving along the ground one second later?
Problem 2: A boat is being pulled into a dock by a rope that passes through a ring on the bow of the boat. The dock is 8 feet higher than the bow ring. How fast is the boat approaching the dock when the length of rope between the dock and the boat is 10 feet, if the rope is being pulled in at the rate of 3 feet per second?
Problem 3: A 5-foot girl is walking toward a 20-foot lamppost at the rate of 6 feet per second. How fast is the tip of her shadow (cast by the lamp) moving?
Problem 4: The equation of free fall of an object (under the influence of gravity alone) is s = s0 + v0t — 16t2, where s0 is the initial position and v0 is the initial velocity at time t=0. Assuming that one story of a building is 10 feet, with what speed, in miles per hour, does an object dropped from the top of a 40-story building hit the ground?
Problem 5:
An object moves along the x-axis so that its x-coordinate obeys the law x = 3t3 + 8t + 1. Find the time(s) when its velocity and acceleration are equal.
#Mathematics #Calculus #HighSchool #College
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Please watch: "Analytic Geometry: 5 Ways to write an equation of the line"
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