MHT CET · Maths · Application of Derivatives
A bullet is shot horizontally and its distance S cm at time t second is given by \(\mathrm{S}=1200 \mathrm{t}-15 \cdot \mathrm{t}^2\), then the distance covered by the bullet when it comes to the rest, is
- A 12000 cm
- B 24000 cm
- C 1200 cm
- D 2400 cm
Answer & Solution
Correct Answer
(B) 24000 cm
Step-by-step Solution
Detailed explanation
\(s=1200 t-15 t^2\)
\(\operatorname{Velocity}(\mathrm{v})=\frac{\mathrm{ds}}{\mathrm{dt}}=1200-30 \mathrm{t}\)
When bullet stopped, \(\frac{\mathrm{ds}}{\mathrm{dt}}=0\)
\(\Rightarrow t=40\)
Hence, required distance
\(=1200(40)-15 \times(40)^2=24000 \mathrm{~cm}\)
\(\operatorname{Velocity}(\mathrm{v})=\frac{\mathrm{ds}}{\mathrm{dt}}=1200-30 \mathrm{t}\)
When bullet stopped, \(\frac{\mathrm{ds}}{\mathrm{dt}}=0\)
\(\Rightarrow t=40\)
Hence, required distance
\(=1200(40)-15 \times(40)^2=24000 \mathrm{~cm}\)
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