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
Algebra.Com
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?
Answer by ankor@dixie-net.com(22740) (Show Source): 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
RELATED QUESTIONS
A turkey is shot up into the air from a height of 18 feet above ground level with an... (answered by lwsshak3)
When an arrow is shot into the air, it’s height, h, in feet above the ground is given... (answered by richwmiller,ikleyn)
My problem is:
An arrow is shot from the top of a 144 foot tower with an initial... (answered by jim_thompson5910)
Ben shoots an arrow. The height of the arrow can be modleled at y=-16x^2 +100x + 4, where (answered by josmiceli)
An arrow is shot vertically upward with an initial velocity of 250 feet per second from... (answered by solver91311)
A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground (answered by mananth,ikleyn)
if a projectile is shot vertically upward from the ground with an initial velocity of 150 (answered by Alan3354)
if a projectile is shot vertically upward from the ground with an initial velocity of 150 (answered by Alan3354,stanbon)
A bullet is shot straight up into the air from ground level. It reaches a maximum height... (answered by ikleyn)