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  4. A projectile is thrown with velocity u=(20 m s- 1)± 5 % at an angle 60o . If the projectile comes back on the ground at the same level then which of the following cannot be a possible answer for range. Consider g=10 ms- 2 .

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Q. A projectile is thrown with velocity $u=\left(20 m s^{- 1}\right)\pm \, 5\%$ at an angle $60^{o} .$ If the projectile comes back on the ground at the same level then which of the following cannot be a possible answer for range.
Consider $g=10 \, ms^{- 2}$ .

NTA AbhyasNTA Abhyas 2022

Solution:

$Range \, of \, projectile \, R=\frac{u^{2} s i n 2 \theta }{g}$
for $ \, \theta = 60^{o} , \, R = \frac{20^{2} sin 120^{o}}{g} = 20 \sqrt{3} = 34.64 \, \text{m}$
$for \, \% \, error\frac{\Delta R}{R}=\frac{2 \Delta u}{u}$
$\text{ΔR} = \frac{2 \times 5}{100} \, \times \, 20 \sqrt{3} = 2 \sqrt{3} = \, 3.464 \, \text{m}$
So, range $\text{R} = 34.64 \pm 3.46 \, \text{m}$
$R_{min}=31.1 \, \text{m}$ and $R_{max \, } 38.1 \, \text{m}$