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A projectile fired vertically up from a cannon rises 200 meters before returning to ground. If the same cannon were to fire the same projectile at an angle, then the maximum range would be approximately (A) 200 m. (B) 400 m. (C) 800 m. (D) 1600 m. (Assume that air resistance is negligible.)

A projectile fired vertically up from a cannon rises 200 meters before returning to ground. If the same cannon were to fire the same projectile at an angle, then the maximum range would be approximately
(A) 200 m.         (B) 400 m.
(C) 800 m.         (D) 1600 m.
(Assume that air resistance is negligible.)
 

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
The correct option is: (B) 400 m.
The range of the projectile fired is given as:
236-95_1.PNG
Here v0 is the magnitude of initial velocity of projectile,\phi _{0} is the angle at which the projectile is fired and g is the acceleration due to gravity.
The maximum height attained by the projectile is given as:
236-2077_2.PNG
Here v0 is the magnitude of initial velocity of projectile and g is the acceleration due to gravity.
The above expression can also be written as:
236-2040_3.PNG
Therefore the maximum range of the projectile is twice the height attained when it was fired vertically.
236-2141_4.PNG
Therefore, the maximum range of the projectile is 400 m and (B) is the correct option.

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