SOLUTION: A girl standing on the ground throws a tennis ball upwards into the air. The height in feet of the ball above the ground t seconds after being thrown is 80t-10t^2. The ball lands o

Question 813712: A girl standing on the ground throws a tennis ball upwards into the air. The height in feet of the ball above the ground t seconds after being thrown is 80t-10t^2. The ball lands on a rood above her 6 seconds after being thrown.
a) How high is the roof? (in feet)
b) What is the velocity upwards of the ball after t seconds? (feet/sec)
c) What was the speed of the ball when it hit the roof? (feet/sec)
d) How high above the roof was the ball when the speed of the ball was zero? (feet)
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
80t-10t^2=0
{t = 8)
a) 80t-10t^2 t=6 120 ft roof
b) -20 (t-4)
c)64.3 ft per sec or using the derivative 40
c) see the table below
d) max height was 160 at 4 seconds
Time
(s) Velocity Distance
m/s km/h ft/s mph m ft
1 9.8 35.3 32.2 21.9 4.9 16.1
2 19.6 70.6 [64.3] 43.8 19.6 64.3
3 29.4 106 96.5 65.8 44.1 144.8
4 39.2 141 128.7 87.7 78.5 257.4
5 49.1 177 160.9 110 122.6 402.2
6 58.9 212 193.0 132 176.6 579.1
7 68.7 247 225.2 154 240.3 788.3
8 78.5 283 257.4 176 313.9 1,029.6
9 88.3 318 289.6 198 397.3 1,303.0
10 98.1 353 321.7 219 490.5 1,608.7

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