Hard
Question
A bomber plane moving at a horizontal speed of 20 m/s releases a bomb at a height of 80 m above ground as shown. At the same instant a Hunter starts running from a point below it, to catch the bomb at 10 m/s. After two seconds he realized that he cannot make it, he stops running and immediately holds his gun and fires in such direction so that just before bomb hits the ground, bullet will hit it. What should be the firing speed of bullet. (Take g = 10 m/s2)
Options
A.10 m/s
B.
m/s
m/sC.
m/s
m/sD.None of these
Solution
In 2 sec. horizontal distance travelled by bomb = 20 × 2 = 40 m.
In 2 sec. vertical distance travelled by bomb =
× 10 × 22 = 20 m.
In 2 sec. horizontal distance travelled by Hunter = 10 × 2 = 20 m.
Time remaining for bomb to hit ground =
− 2 = 2 sec.
Let Vx and Vy be the velocity components of bullet along horizontal and vertical direction.
Thus we use,
= 2 ⇒ VY = 10 m/s and 
= 2 ⇒ Vx = 30 m/s
Thus velocity of firing is V =
= 
In 2 sec. vertical distance travelled by bomb =
× 10 × 22 = 20 m.In 2 sec. horizontal distance travelled by Hunter = 10 × 2 = 20 m.
Time remaining for bomb to hit ground =
− 2 = 2 sec.Let Vx and Vy be the velocity components of bullet along horizontal and vertical direction.
Thus we use,
= 2 ⇒ VY = 10 m/s and = 2 ⇒ Vx = 30 m/sThus velocity of firing is V =
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