An arrow is shot vertically upward from a platform 16ft high at a rate of 190ft/sec. When will the arrow hit the ground? Use the formula: h=-16t²+vt+h0. (Round your answer to the nearest tenth.)

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

H (t) = - 16t2 + 186t + 43

at the ground h = 0

hence; - 16t2 + 186t + 43 = 0

solving this quadratic equation using the quadratic formula; a = - 16, b = 186, c = 43; x = (-b + - (b2 - 4ac) 1/2) / 2a

gives t = 11.8 seconds to the nearest tenth (note that the negative root has no practical significance)