Answer:
a) 8 seconds
b) 3 seconds
c) 170 meters
Step-by-step explanation:
a) When the ball lands in the sea, s = -80.
-80 = 30t − 5t²
5t² − 30t − 80 = 0
t² − 6t − 16 = 0
(t + 2) (t − 8) = 0
t = -2 or 8
t = 8 seconds
b) The ball reaches its highest point when the velocity is 0 (or at the vertex of the parabola).
t = -b / (2a)
t = -30 / (2 × -5)
t = 3 seconds
c) The highest point is:
s = 30(3) − 5(3)²
s = 45
So the ball rises 45 meters, falls 45 meters, then falls 80 meters.
The total distance traveled is 45 + 45 + 80 = 170 meters.
