SOLUTION: An astronaut on the moon tosses a ball upwards; when will the ball initially be 35 feet above the lunar surface if the ball's height (feet) follows: h(t) = -2.6t^2 + 32.1t + 5.5, a

Algebra ->  Equations -> SOLUTION: An astronaut on the moon tosses a ball upwards; when will the ball initially be 35 feet above the lunar surface if the ball's height (feet) follows: h(t) = -2.6t^2 + 32.1t + 5.5, a      Log On


   

Question 147563: An astronaut on the moon tosses a ball upwards; when will the ball initially be 35 feet above the lunar surface if the ball's height (feet) follows: h(t) = -2.6t^2 + 32.1t + 5.5, and t is in seconds from release?
a. 1 second
b. 2 seconds
c. .5 seconds
d. 13.2 seconds
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
h%28t%29+=+-2.6t%5E2+%2B+32.1t+%2B+5.5 Start with the given equation.


35+=+-2.6t%5E2+%2B+32.1t+%2B+5.5 Plug in h%28t%29=35


10%2835%29=10%28-2.6t%5E2%2B32.1t%2B5.5%29 Multiply both sides by 10 to clear out the decimals.


350=-26t%5E2%2B321t%2B55 Distribute and multiply.


0=-26t%5E2%2B321t%2B55-350 Subtract 350 from both sides.


0=-26t%5E2%2B321t-295 Combine like terms.


Let's use the quadratic formula to solve for t


t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


t+=+%28-%28321%29+%2B-+sqrt%28+%28321%29%5E2-4%28-26%29%28-295%29+%29%29%2F%282%28-26%29%29 Plug in a=-26, b=321, and c=-295


t+=+%28-321+%2B-+sqrt%28+103041-4%28-26%29%28-295%29+%29%29%2F%282%28-26%29%29 Square 321 to get 103041.


t+=+%28-321+%2B-+sqrt%28+103041-30680+%29%29%2F%282%28-26%29%29 Multiply 4%28-26%29%28-295%29 to get 30680


t+=+%28-321+%2B-+sqrt%28+72361+%29%29%2F%282%28-26%29%29 Subtract 30680 from 103041 to get 72361


t+=+%28-321+%2B-+sqrt%28+72361+%29%29%2F%28-52%29 Multiply 2 and -26 to get -52.


t+=+%28-321+%2B-+269%29%2F%28-52%29 Take the square root of 72361 to get 269.


t+=+%28-321+%2B+269%29%2F%28-52%29 or t+=+%28-321+-+269%29%2F%28-52%29 Break up the expression.


t+=+%28-52%29%2F%28-52%29 or t+=++%28-590%29%2F%28-52%29 Combine like terms.


t+=+1 or t+=+295%2F26 Simplify.


So our answers are t+=+1 or t+=+295%2F26


where the second answer approximates t+=+11.346


So when the ball is initially at 35 feet, the time is t+=+1.