Question

A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given by the polynomial h = 25t − 5t². 

Observe the graph of the polynomial and answer the following questions:

1. Write zeroes of the given polynomial.    [1]
2. Find the maximum height achieved by ball.     [1]
3. 
   
   1. After throwing upward, how much time did the ball take to reach to the height of 30 m?    [2]
                                OR 
   2. Find the two different values of t when the height of the ball was 20 m.    [2]

Answer 1

i. Two  [The point at which the curve touch the x-axis is zero's]

Here, x = 0, 5

ii. Given h = 25t − 5t²

Maximum height at a point `(5/2, 0)`

`h = 25 xx 5/2 - 5(5/2)^2`

= `125/2 - 125/4`

= 62.5 − 31.25

= 3.25

h = 31.25

iii.

(a) Ball take time to reach a height 30 m 

30 = 25t − 5t²

5t² − 25t + 30 = 0

⇒ t² − 5t + 6 = 0 

⇒ t² − 3t − 2t + 6 = 0

(t − 3) (t − 2) = 0 

t = 3, 2

(b) when height is = 20 m 

20 = 25t − 5t²

⇒ 5t² − 25t + 20 = 0

⇒ t² − 5t + 4 = 0 

t² − 4t − t + 4 = 0 

(t − 4) (t − 1) = 0 

t = 4, 1