Solving word problems using derivatives

[Danatron]

Hi Guys,

I am revising for an exam i have this week, the last module on my subject was calculus. I did not understand it entirely.

I have posted a pic below of a typical problem i can expect to encounter, would anybody be able to point me in the right direction to study material that could teach me how to solve problems like this? my lecture is very vague and study material even vaguer.

 

[symbolipoint]

Applications of derivatives, found in typical first-year undergraduate Calculus textbooks. h(t) takes the shape (as a cartesian graph) of a parabola with vertex as a maximum. The positive root will be the time when the ball reaches the ground. You can use the first derivative of h, equate this derivative to zero, solve this for t, and that is the time when h is the maximum.

 

[Matterwave]

Which part of the problem is most difficult to you? Conceptually understanding what the question is asking? Or is it the math? Or is it the physical intuition?

The best way to study for exams is different for everybody. It's hard to point you in the direction of the study material if I don't know what you want to study. Do you want to study calculus (how to take derivatives, etc.)? Or do you want to study kinematics?

It might be useful to just find some books with a lot of practice problems similar in difficulty to the ones you will encounter. Have you tried working through the problems in your textbook? Usually introductory physics textbooks will have a lot of practice problems you can do.

 

[symbolipoint]

Also note that dh/dt is a velocity function, so you can use it to determine the velocity for when t is the positive root (meaning, the ball hits the ground).

 

[Arka420]

Also note that dh/dt is a velocity function, so you can use it to determine the velocity for when t is the positive root (meaning, the ball hits the ground).

How to differentiate that h₀ term? Chain rule?

 

[phion]

You want to find the relative maximum, a value of t where the derivative of the position function is equal to zero, and the second derivative is negative, then, as mentioned, determine the value of h(t) just before it reaches the positive zero.

 

[SteamKing]

How to differentiate that h₀ term? Chain rule?

h_{0} and v_{0} are just constants; the independent variable in the equation is t.

 

[TitoSmooth]

Reember that h (t)= s (t) this is called the position function.

The derivative h`(t)=v (t) this is called the velocity function

The derivative of h'(t) is h''(t) where h''(t)=a (t) this is called the acceleration function.


Use all 3 functions to solve specific given statements. Understand what it means by position, velocity, and acceleration.