Problema Solution
A projectile is fired upward from ground level with an initial velocity of 85 ft/sec. The equation h=-16t^2 85t represents this situation
a.) The the nearest tenth of a second, how long until the object first reaches a height of 56 feet?
b.) How long until the object is again at 56 feet?
c.) How many seconds until it returns to the ground?
Answer provided by our tutors
a.) The the nearest tenth of a second, how long until the object first reaches a height of 56 feet?
h=-16t^2 + 85t
we need to find t such that h = 56 that is
-16t^2 + 85t = 56
by solving we find:
t = 0.77 s
click here to see the step by step solution of the quadratic equation:
there are 2 roots of the quadratic equation since the projectile reaches height of 56 ft once when going up and second time when falling down. we need the smaller root (the time it needs to reach the height).
b.) How long until the object is again at 56 feet?
t = 4.54 s
it is the second root of the quadratic equation above.
c.) How many seconds until it returns to the ground?
when the projectile reaches the ground when h = 0 and t <>0 thus we solve the equation:
-16t^2 + 85t = 0
and find:
t = 5.31 s
click here to see the step by step solution of the equation:
the projectile reaches the ground in 5.31 seconds.