Answer:
time required for arrow to reach ground is 10.8 sec
when t = 10.8 seconds to the nearest tenth
Step-by-step explanation:
Given values are
Velocity = 190 ft/sec height = 16 ft
Given formula is
h=−16t²+vt+h0
adding the values, we get
h(t)= -16t²+190t+16
so we have to find when the hit he ground, so at ground the height will be 0
0= -16t²+190t+16
-16t²² + 190t + 16= 0
using the quadratic formula
x = (-b +(b2 - 4ac)1/2)/2a
values
a = -16, b = 190, c = 16
x= -190 + ((-190)²- 4 (-16)(16) ½ / 2(-16)
x= -190 + ((-190) ²+1024) ½ / 2(-16)
x= -190+ (-190²+ 32²) ½ /-32
taking under root
x= -190 + ( -190+32)/ -32
x= 190 + (-158)/-32
we have 2 options,
x= 190 + (-158)/-32 x= 190 - (-158)/-32
x= 190 -158)/-32 x= 190 +158)/-32
x= -1 x= 10.875
or t = 10.875
so the negative root has no practical significance
and we have t = 10.8 seconds to the nearest tenth
