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Answer 1

Question:

• A stone is thrown vertically downwards and the formula d = 16t² + 4t gives the distance, d metres , that it falls in t seconds. How long it take to fall 420 metres? .

Information given to us:

• d = 16t² + 4t

What we have to calculate:

• Time taken by the stone to fall 420 metres

Equation formed:

As we have distance (d) is 420 m

• 16t² + 4t = 420

Solving now:

• Reversing the sides:

→ 16t² + 4t - 420 = 0

• Taking common as 4:

→ 4 (4t² + t - 105)

• Dividing them by 4:

→ 4 (4t² + t - 105) / 4 = 0

→ 4t² + t - 105 = 0

• Forming factors,

→ 4t² - 20t + 21t - 105 = 0

• Grouping them,

→ 4t (t - 5) + 21 (t - 5) = 0

→ (4t + 21) (t - 5) = 0

Comparing both:

• t - 5 = 0
• t = 5

And,

• 4t + 21 = 0
• 4t = -21
• t = -21/4

Hence,

• It takes 5 seconds to fall 420 metres

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