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Grade 11Mechanics

During the Battle of Tarawa in World War II, battleships fired ballistic projectiles at the Japanese garrisons on Betio from as far as 40 miles out at sea. Assuming no air resistance, and assuming the trajectories were chosen to give the optimum range,
(a) the projectiles would have risen to a maximum altitude in the range of
(A) 0 to mi. (B) (C) 2 to 5 mi. (D) 5 to 8 mi.
(E) 8 to 12 mi.
Before returning to the ground.
(b) What would be the approximate muzzle velocity of the projectiles?
(A) 25,000 ft/s. (B) 2,500 ft/s.
(C) 250 ft/s. (D) 25 ft/s.

Simran Bhatia

11 Years agoGrade 11

1 Answer

Aditi Chauhan

11 Years ago

(a)
The correct option is: (D) 5 to 8 mi.
(b)
The correct option is: (B) 2,500 ft/s.
(a)
The optimum range for the battleships as far as 40 mi is given as:

Here, v₀ is the muzzle velocity of the projectile, $\theta$ is the angle at which the projectile is fired (relative to horizontal) and g is the free fall acceleration.
Substitute 40 mi for R,

Also, the height or altitude of the projectile corresponding to the same angle $\theta$ and muzzle velocity v₀ is given as:

Therefore the maximum altitude for the optimum range of battleships 40 mi away is 10 mi. Raising the altitude more by keeping the variable v₀ as constant decreases the range of the projectile and therefore the correct option is likely to be 5 to 8 mi corresponding to
option (D).

The closest value to above answer is 2,500 ft / s and therefore the correct option is (B).

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