﻿ How long until object hits the ground? - science mathematics
How long until object hits the ground?

## How long until object hits the ground?

[From: Physics] [author: ] [Date: 01-07] [Hit: ]
How long until object hits the ground?A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial func......

How long until object hits the ground?
A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial function P(t) = ­16t2 + 300t How long will it be until the object hits the ground? I realize that my teacher...
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answers:
Steve4Physics say: h(t) = -16t² +300t+ h can’t be correct as you have h on both sides of the equation and h would cancel. But you are correct to put the minus sign in. h(t) = -16t² +300t.

When the object hits the ground h=0, so we just have to solve:
-16t² +300t = 0

75t – 4t² = 0 (divided-through by 4 and rearranged)
t(75 – 4t) = 0 (factorised)

t = 0 or t = 75/4 = 18.75s (=19s to 2 sig. figs.)

t = 0 corresponds to the time the projectile is fired; t = 19s is the time it returns to the ground.
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electron1 say: You are correct. The projectile’s acceleration is negative. The following equation is used to solve this problem.

ht = -½ * g * t^2 + 300 * t
½ * g = 16
g = 32 ft/s^2

a = -32 ft/s

During one half of the total time, the projectile’s velocity decreases from 300 m/s to 0 m/s. Let’s use the following equation to determine the time for this to happen.

vf = vi + a * t
0 = 300 + -32 * t
t = 300 ÷ 32 = 9.375 seconds
Total time = 18.75 seconds

I hope this is helpful for you.
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say: At 300 ft/sec and a downward acceleration due to gravity of 32.2 ft/sec^2, it takes 300 ft/sec / 32.2 ft/sec^2 = 9.32 sec to reach the top of the arc where its velocity = 0. The trip back takes the same amount of time.

2 * 9.32 sec is the total time.
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