SOLUTION: An arrow shot vertically into the air from ground level with a crossbow reaches a maximum height of 324 feet after 4.5 seconds of flight. Let the quadratic function d(t) represent
Question 723515: An arrow shot vertically into the air from ground level with a crossbow reaches a maximum height of 324 feet after 4.5 seconds of flight. Let the quadratic function d(t) represent the distance above ground (in feet) t seconds after the arrow is released. (If air resistance is neglected, a quadratic model provides a good approximation for the flight of a projectile.)
(A) Find d(t)
(B) At what times (to two decimal places) will the arrow be 250 feet above the ground?
You can put this solution on YOUR website! An arrow shot vertically into the air from ground level with a crossbow reaches a maximum height of 324 feet after 4.5 seconds of flight. Let the quadratic function d(t) represent the distance above ground (in feet) t seconds after the arrow is released. (If air resistance is neglected, a quadratic model provides a good approximation for the flight of a projectile.)
:
(A) Find d(t)
Find the initial velocity (v) of the arrow using the form -16t^2 + vt = d(t)
t=4.5, d(t)= 324
-16(4.5^2) + 4.5v = 324
-16(20.25) + 4.5v = 324
-324 + 4.5v = 324
4.5v = 324 + 324
4.5v = 648
v = 648/4.5
v = 144 ft/sec is the initial upward velocity of the arrow
the equation
d(t) = -16t^2 + 144t
:
(B) At what times (to two decimal places) will the arrow be 250 feet above the ground?
-16t^2 + 144t = 250
-16t^2 + 144t - 250 = 0
Solve for t using the quadratic formula,
I got t = 2.35 and 6.65 sec at 250 ft
:
Graphically, green line is 250 ft, blue line is 324 ft
