You must solve equation:
- 16 t ^ 2 + 64 t + 80 = 0
- 16 t ^ 2 + 64 t + 80 = 0 Divide both sides by - 16
- 16 t ^ 2 / - 16 + 64 t / - 16 + 80 / - 16 = 0
t ^ 2 - 4 t - 5 = 0 Add 5 to both sides
t ^ 2 - 4 t - 5 + 5 = 0 + 5
t ^ 2 - 4 t = 5 Add 4 to both sides
t ^ 2 - 4 t + 4 = 5 + 4
t ^ 2 - 4 t + 4 = 9
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Remark :
t ^ 2 - 4 t + 4 = ( t - 2 ) ^ 2
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( t - 2 ) ^ 2 = 9 Take the square root of both sides
t - 2 = - 3
and
t - 2 = 3
t - 2 = - 3 Add 2 to both sides
t - 2 + 2 = - 3 + 2
t = - 1 s
t - 2 = 3 Add 2 to both sides
t - 2 + 2 = 3 + 2
t = 5 s
Solutions:
t = - 1 a and t = 5 s
Time cant be negative so : t = 5 s
Proof:
- 16 t ^ 2 + 64 t + 80 =
- 16 * 5 ^ 2 + 64 * 5 + 80 =
- 400 + 320 + 80 = 0
(h=-16t^2+64t+80), after how many seconds will the object hit the ground at the bottom of the cliff.
1 answer