Question

A stone is thrown into air from the top of a building of height h m. The height of the stone (in metres) above the ground after t seconds is given by h (t) = 5t² + 30t + 2; where 't' is the time from when the stone is thrown.

1. How high will the stone be from the ground after 2 seconds?
2. From what height, above the ground, the stone is thrown?
3. At what time will the stone be 37 m above the ground?

Answer 1

(i) Given,

The height of the stone above the ground after t seconds: h (t) = 5t² + 30t + 2

t = 2

Substituting value of t = 2 in h(t):

⇒ h(2) = 5(2)² + 30(2) + 2

= 5(4) + 60 + 2

= 20 + 60 + 2

= 82 m.

Hence, the height after 2 seconds is 82 m.

(ii) The initial height of stone,

Substituting value of t = 0 in h(t):

⇒ h(0) = 5(0)² + 30(0) + 2

= 2 m.

Hence, stone is thrown from a height of 2 m.

(iii) Given,

h(t) = 37

⇒ 5t² + 30t + 2 = 37

⇒ 5t² + 30t + 2 − 37 = 0

⇒ 5t² + 30t − 35 = 0

⇒ 5(t² + 6t − 7) = 0

⇒ t² + 6t − 7 = 0

⇒ t² + 7t − t − 7 = 0

⇒ t(t + 7) − 1(t + 7) = 0

⇒ (t − 1)(t + 7) = 0

⇒ (t − 1) = 0 or (t + 7) = 0

⇒ t = 1 or t = −7

Since time cannot be negative,

t = 1 second.

Hence, stone will be 37 m above the ground after 1 second.