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  4. A fighter plane enters inside the enemy territory, at time t=0 with velocity v0=250 m s- 1 and moves horizontally with constant acceleration a=20 m s- 2 (see figure). An enemy tank, at the border, spots the plane and fire shots at an angle θ =60° with the horizontal and with velocity u=600 m s- 1 .The altitude H , where the plane can be hit by the shot, is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-qzwl78durv7z.png />

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Q. A fighter plane enters inside the enemy territory, at time $t=0$ with velocity $v_{0}=250 \, m \, s^{- 1}$ and moves horizontally with constant acceleration $a=20 \, m \, s^{- 2}$ (see figure). An enemy tank, at the border, spots the plane and fire shots at an angle $\theta =60^\circ $ with the horizontal and with velocity $u=600 \, m \, s^{- 1}$ .The altitude $H$ , where the plane can be hit by the shot, is



Question

NTA AbhyasNTA Abhyas 2020Motion in a Plane

Solution:

If being hit, then horizontal distance remains same.
Solution
$v_{x}=\text{600 cos 60}^{\text{ο}}=300ms^{- 1}$
$\left(250 \mathrm{~m} \mathrm{~s}^{-1}\right) \mathrm{t}+\frac{1}{2}(20) \mathrm{t}^2=300 \mathrm{t}$
$\left(\text{50 t}\right) = \frac{1}{2} \left(\text{20}\right) t^{2}$
$\text{t} = 0$ or $\text{t} = 5$
$\text{H} = \left(\left(\text{600}\right) \left(\text{sin 60}\right)^{\text{ο}}\right) t - \frac{1}{2} g t^{2}$
$=\left(\text{600}\right)\frac{\left(\sqrt{3}\right)}{2}\times 5-\frac{1}{2}\cdot \left(10\right)\left(\text{25}\right)$
$\text{H}=\left(\text{300} \sqrt{3}\right) 5 - \left(\text{125}\right)m$
$H=2473m$