When will the height be 447 feet? When will the object reach the ground?

Question

An object is thrown upward at a speed of 170 feet per second by a machine from a height of 8 feet off the ground. The height h of the object after t seconds can be found using the equation h= -16t^2 + 170t + 8

When will the height be 447 feet?

When will the object reach the ground?

Answer 1

Hi Ashley,

An object is thrown upward at a speed of 170 feet per second by a machine from a height of 8 feet off the ground. The height h of the object after t seconds can be found using the equation h= -16t² + 170t + 8

When will the height be 447 feet?

When will the object reach the ground?

Given:

1. thrown upward 170 ft/s
2. 8feet off the ground to start
3. Equation: h= -16t² + 170t + 8

Find:

1. When will the height be 447 feet?
2. When will the object reach the ground?

When you throw an object up in the air, it will travel slowing down until it reaches a maximum height, stop, then drop back down to the ground.

You are asked to find the time it will take to reach 447 feet.

Use the equation given and substitute 447 for h. Solve for t

h= -16t² + 170t + 8

447ft = -16t² + 170t + 8

-16t² + 170t + -439=0

To solve I'll use ax²+bx +c x= [-b ±√(b²-4ac) ] / 2a

x=[ -170±√(170)²-4(-16)(-439) ] / 2(-16)

x = [-170+√804] / -32 x=[-170-√804] / -32

x = 6.20s x= 4.43s

There are two answers to this because the object rises into the air, gets to 447 ft and then continues upward. After it peaks and heads back down, it falls to 447 ft again on the way down.

Based on the wording of the question, I'm assuming it means the first time it reaches 447 ft. The first time it reaches 447 feet is at 4.43s

Time to reach 447 ft = 4.43s

The next question to answer: When will the object reach the ground? Well, to determine that, you would set the value for height in the equation as 0.

h= -16t² + 170t + 8

0= -16t² + 170t + 8

To solve I'll use ax²+bx +c x= [-b ±√(b²-4ac) ] / 2a

[-170±√170²-4(-16)(8)] / 2(-16)

[-170± √29412] / -32

t=-0.047 s t= 10.67s

There are again two answers that need to be evaluated. The height is 8ft at the start. When you hit the ground you are at 0 feet. The first answer was a negative time. This one is not valid. (It's the time you would have had to start if the object started from the ground)The second time is 10.67s. This time is when the object rose up in the air then fell.

When will the object reach the ground?

t=10.67s

Let me know if you have more questions!!