A ball is hit vertically upwards from a cliff, which is 80 m above the sea. The displacement from the edge of the cliff, s, measured upwards in metres, after t seconds is given by
S = 300 - 5t2. Calculate:
a the time it takes for the ball to land in the sea
b the time it takes to reach the highest point
c the total distance travelled during the motion.

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.

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490