Question

If an object is launched from a point 15 m above the ground with an initial upward velocity of 25 m/s, how much time will pass before it returns to the ground? (Ignore air resistance.)

Answer 1

Do you know 1D Kinematic formulas?

Answer 2

I know of them but I'm not sure which one to use.

Answer 3

The best way is to write down your knowns and what unknown you're trying to find

So you have initial vertical velocity and height relative to the ground and you want to find the time

Use the equation that uses initial velocity and height, and has time in it

Answer 4

x = x0 +v0t + ½ at2

Answer 5

but if i use this equation, what do i plug in for the x that is not relevant to initial position?

Answer 6

Try breaking the problem down into two. The first part would be from the initial point to the highest point, then from the highest point to the ground.

Answer 7

i'm not sure how to do that using the kinematic formulas. is it possible to figure it out using the relationship of derivatives? like how velocity is the derivative of position, and acceleration is the derivative of velocity?

Answer 8

so far, for the position equation, i got: x(t)=25t + 15. does that seem right?

Answer 9

No, that's unneccesary because the kinematic equations are already derived using calculus.

Also you are forgetting acceleration due to gravity

Answer 10

i'm confused, then how do i break the problem into two using the kinematic equations? and was the equation i chose even the right one to use?

Answer 11

There are usually multiple solutions. But it helps to draw the problem: