Can someone please explain how to do this problem?

Cadets graduating from military school usually toss their hats high into the air at the end of the ceremony. One cadet threw his hat so that its distance d( t )= #-16t^2# + 30t + 6.
a. Find the distance above the ground of the hat 1 second after it was thrown.
b. Find the time it took that hat to hit the ground. Give the exact time and a one-decimal-place approximation.

Cadets graduating from military school usually toss their hats high into the air at the end of the ceremony. One cadet threw his hat so that its distance d( t )= #-16t^2# + 30t + 6.
a. Find the distance above the ground of the hat 1 second after it was thrown.
b. Find the time it took that hat to hit the ground. Give the exact time and a one-decimal-place approximation.

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

2
Nov 19, 2017

Answer:

a. #20# #m#.
b. #2.06# #s#.

Explanation:

To find the height you only have to substitute #t# in the equation for the number of seconds you what to know its possition,
#d(t)=-16·1^2+30·1+6=20# #m#

and to find the time it took the hat to hit the ground you need to think a bit. If the hat is in the ground it means that de height is #0#, so you can equal the equation to #0# and find the value of #t#.
#-16t^2+30t+6=0#

we can use the formula for quadratics equations.
#t=(-b+-sqrt(b^2-4ac))/(2a)=(-30+-sqrt(30^2-4·(-16)·6))/(2·(-16))=#
#=(-30+-sqrt(900+384))/(-32)=(-30+-sqrt(1284))/(-32)#

#cancel(t_1=(-30+sqrt(1284))/(-32)=-0.18s)#
This solution is not possible because time can't be negative.

#t_2=(-30-sqrt(1284))/(-32)=2.06# #s#

Was this helpful? Let the contributor know!
1500