Question:
At the height $80\, m$ , an aeroplane is moved with $150\,m/s$. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? (given $g=10\,m/s^{2}$)
At the height $80\, m$ , an aeroplane is moved with $150\,m/s$. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? (given $g=10\,m/s^{2}$)
Updated On: Jul 5, 2022
- 605.3 m
- 600 m
- 80 m
- 230 m
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The Correct Option is B
Solution and Explanation
Time taken by the bomb to reach the ground is given by
$t=\sqrt{\left(\frac{2 h}{g}\right)}$
$t=\sqrt{\left(\frac{2 \times 80}{10}\right)}=4\, \sec$
Horizontal velocity of bomb $=150\, m / s$
Horizontal distance covered by bomb $=150 \times 4=600\, m$
Hence, the bomb should be dropped $600\, m$ before the target.
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration