SOLUTION: Help! I need an answer quickly for this: Susie throws a ball from a starting height of 10 feet upwards at an initial velocity of 30 ft/sec. How long will it take for the ball to

Algebra ->  Expressions-with-variables -> SOLUTION: Help! I need an answer quickly for this: Susie throws a ball from a starting height of 10 feet upwards at an initial velocity of 30 ft/sec. How long will it take for the ball to      Log On


   

Question 873129: Help! I need an answer quickly for this:
Susie throws a ball from a starting height of 10 feet upwards at an initial velocity of 30 ft/sec. How long will it take for the ball to hit a target 15 ft high?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solve -16t%5E2+%2B+30t+%2B+10+=+15 for t (using any method) to get these approximate solutions t+=+0.1849003388 or t+=+1.690099661


So it will take 0.1849003388 seconds for it to hit the 15 ft mark. It will pass the 15 ft marker and then come back down to the 15 ft marker at 1.690099661 seconds.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation would be:
+h%28t%29+=+-16t%5E2+%2B+30t+%2B+10+
+h+ is height in feet, and +t+ is time in seconds
----------------------------
You need to know when +h%28t%29+=++15+ ft
+15+=+-16t%5E2+%2B+30t+%2B+10+
+-16t%5E2+%2B+30t+-+5+=+0+
Use the quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-16+
+b+=+30+
+c+=+-5+
+t+=+%28-30+%2B-+sqrt%28+30%5E2-4%2A%28-16%29%2A%28-5%29+%29%29%2F%282%2A%28-16%29%29+
+t+=+%28-30+%2B-+sqrt%28+900+-+320+%29%29%2F%28-32%29+
+t+=+%28+-30+%2B-sqrt%28+580+%29+%29+%2F+%28-32%29+
+t+=+%28+-30+%2B+24.0832+%29+%2F+%28+-32+%29+
+t+=+5.9168+%2F+32+
+t+=+.185+
It will take the ball .185 sec to hit the target
check answer:
+15+=+-16t%5E2+%2B+30t+%2B+10+
+5+=+-16%2A.185%5E2+%2B+30%2A.185+
+5+=+-16%2A.034225+%2B+5.55+
+5+=+-.5476+%2B+5.55+
+5+=+5.0024+
close enough