Additional Mathematics – Calculus | e-Consult
Calculus (1 questions)
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Differentiate: dh/dt = 20 – 10t. Set to zero for a maximum:
20 – 10t = 0 → t = 2 s.
Maximum height: h(2) = 20·2 – 5·(2)² = 40 – 20 = 20 m.
To find when the ball returns to ground, solve h(t)=0:
20t – 5t² = 0 → t(20 – 5t)=0 → t = 0 or t = 4 s.
The ball reaches its maximum height of 20 m at t = 2 s and lands after 4 s.