SOLUTION: A person throws a ball upward into the air with an initial velocity of 15 m/s. a.) Calculate how high it goes. Ignore air resistance. (b) how long is the ball in the air before it

Question 1168960: A person throws a ball upward into the air with an initial velocity of 15 m/s. a.) Calculate how high it goes. Ignore air resistance. (b) how long is the ball in the air before it comes back to the hand?
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

The height,

, as a function of time,

, neglective air resistance for a projectile near the surface of the earth (gravitational acceleration in the MKS system

)with a vertical component of initial velocity equal to

and an initial height equal to

is:

Note that

is a negative value because gravitational acceleration is toward the center of the massive body.

The extreme value of this function occurs at

which is the independent variable value that makes the first derivative of the function equal to zero. This extreme value is a maximum if the second derivative is negative at that point.

So solve:

for

noting that

which is a constant

so the extremum is a maximum.

The time that the projectile is in the air is the positive zero of the function. So set the function equal to zero and solve the quadratic. Of course, your difficulty is that you don't know how high off the ground the ball was when the person throwing it released it. So you only have a very vague idea of what the value of

might be.

Good luck.

John

My calculator said it, I believe it, that settles it

I > Ø

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