maths...

👨🏻‍🏫 學術台數學

Yim Yi

2006-10-15 2:11 am

1. a stone was thrown vertically upwards from the ground. Its height above the ground, y metres, reached in x seconds was given by y=20x-5x^2. Find

a) the time the stone took to reach the ground again;
b) the greatest height reached;
c) the average speed of the stone during the flight.

更新1:

可以解釋一下a)嗎??不是很明白...

回答 (1)

Lau

2006-10-15 2:27 am

✔ 最佳答案

a)
y=0 when the stone reaches the ground
ie. 20x-5x^2 = 0
5(4-x)x = 0
x = 0 (rejected) or x = 4
Therefore, it reaches the ground in 4 seconds

b)
y = 20x-5x^2
= 5(4x-x^2)
= 5[-(2)^2+4x-x^2]+20
= -5(x-2)^2+20

Therefore, the greatest height = 20m when x = 2s

c)
distance travelled = 20 * 2 = 40m
time travelled = 4s

Therefore, average speed = 40/4 = 10 m/s

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