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.

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98