Question

An arrow is shot vertically upward at a rate of 160 feet per second from ground level. Use the projectile formula

h
=
−
16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 114 feet.

Answer 1

0.772 seconds; 9.228 seconds

Explanation:

The given projectile formula with the given numbers filled in is ...

`\displaystyle h=-16t^2+v_0t+h_0\\\\114=-16t^2+160t`

We can "complete the square" to solve this for t, the times at which the height is 114 feet.

16(t² -10t) = -16(7.125) . . . . . rearrange, showing factor of 16

t² -10t +25 = -7.125 +25 . . . . divide by 16, add 25 to complete the square

t = 5 ±√17.875 ≈ 5 ± 4.228 . . . . take the square root, add 5

t ∈ {0.772, 9.228}

The arrow is 114 feet high after 0.772 seconds and again after 9.228 seconds.