Projectile Flight

Sep 2008
43
0
Okay so I have this problem and am not sure where to start. Can anyone help?:

An arrow shot verticaly into the air from ground level with a cross bow reaches a maximum height of 484 feet after 5.5 seconds of flight. Let the quadratic function d(t) represent the distance above ground in feet t seconds after the arrow is released.

(a)Find d(t) and state its domain.
(b)At what times (to two decimal places) will the arrow be 250 ft. above the ground?
 

e^(i*pi)

MHF Hall of Honor
Feb 2009
3,053
1,333
West Midlands, England
Okay so I have this problem and am not sure where to start. Can anyone help?:

An arrow shot verticaly into the air from ground level with a cross bow reaches a maximum height of 484 feet after 5.5 seconds of flight. Let the quadratic function d(t) represent the distance above ground in feet t seconds after the arrow is released.

(a)Find d(t) and state its domain.
(b)At what times (to two decimal places) will the arrow be 250 ft. above the ground?
Use the kinematic equations. In this case initial speed is not known, final speed is known (it stops before falling), the height and the time are all known so the following equation is known and can be used to find u.

\(\displaystyle s = ut + \frac{1}{2}at^2\)

This is already a quadratic in t. For the domain think about time, do you get negative time for arrows?

For b set s to 250 and solve for t