Arock is dropped from a bridge 320 feet above the river. the pathway that the rock takes can be modeled by the equation h= -16t2+320. how long will it take the rock to reach the river?

a
2.5 seconds

b
3.5 seconds

c
3.8 seconds

d
4.5 seconds

The rock will take about 4.5 seconds to reach the river

Step-by-step explanation:

* lets study the situation of the rock

- The rock is dropped means the initial velocity is zero

- The motion is free fall under earth gravity

- The rock dropped from a bridge 320 feet above the river

- The equation of the pathway is h = -16t² + 320

- When the rock reach to the ground the height will be zero

* Now lets substitute h by zero in the equation to find t

∵ h = -16t² + 320

∵ h = 0

∴ 0 = -16t² + 320 ⇒ add 16t² to both sides

∴ 16t² = 320 ⇒ divide both sides by 16

∴ t² = 320/16 = 20

∴ t² = 20 ⇒ take √ for both sides

∴ t = √20 = 2√5 ≅ 4.5 seconds

* The rock will take about 4.5 seconds to reach the river