Velocity: A projectile is fired directly upward from...

[katie9426]

I need to find the velocity at the moment of impact given the following information.

A projectile is fired directly upward from ground level with an initial velocity of 112 ft/sec, and its distance above the ground after "t" seconds is given by the equation s(t)=112t - 16t^2 feet

I know you have to set the postion function equal to zero, but that leaves two verables so I'm stuck! Thanks for any help anyone can give!

 

[skeeter]

I know you have to set the postion function equal to zero, but that leaves two verables

what two variables?

set s(t) = 0 ...

112t - 16t² = 0

16t(7 - t) = 0

time of impact is t = 7 seconds

v(t) = s'(t) = 112 - 32t

v(7) = 112 - 32(7) = -112 ft/s

 

[plusC]

Re: Velocity

Finding the derivative of a position function will give you the function for its velocity (and the derivative of the velocity function, and consequently the second derivative of the position function, will give you the function corresponding to acceleration, but we don't need that).

s(t)=112t - 16t^2 (differentiate to find v(t))
v(t)=112-32t

From there you can use the information in the position function to find v(t) which will be your answer.