Motion in a Plane
- Two bodies of same mass are projected with the same velocity at an angle 30° and 60° respectively. The ratio of their horizontal ranges will be
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Horizontal range is same when angle of projection is θ or (90° – θ).
Correct Option: A
Horizontal range is same when angle of projection is θ or (90° – θ).
- The maximum range of a gun of horizontal terrain is 16 km. If g = 10 ms–2, then muzzle velocity of a shell must be
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Rmax = v2 = 16000 [ 6 km = 16000 m ] g
or v = (16000 g)1 / 2 = (16000 × 10)1 / 2
= 400 ms –1Correct Option: C
Rmax = v2 = 16000 [ 6 km = 16000 m ] g
or v = (16000 g)1 / 2 = (16000 × 10)1 / 2
= 400 ms –1
- If a body A of mass M is thrown with velocity v at an angle of 30° to the horizontal and another body B of the same mass is thrown with the same speed at an angle of 60° to the horizontal, the ratio of horizontal range of A to B will be
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Horizontal range is same when angle of projection with the horizonatal is θ and (90° – θ).
Correct Option: B
Horizontal range is same when angle of projection with the horizonatal is θ and (90° – θ).
- Two projectiles are fired from the same point with the same speed at angles of projection 60° and 30° respectively. Which one of the following is true?
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Given, u1 = u2 = u, θ1 = 60° , θ2 = 30°
In 1st case, we know that rangeR1 = u2 sin 2(60°) = u2 sin 120° g g = u2 sin(90° + 30°) g = u2 (cos 30°) = √3 u2 g 2g
In 2nd case, when θ2 = 30° , thenR2 = u2 sin 60° = √3 u2 ⇒ R1 = R2 g 2g
[we get same value of ranges].
Correct Option: B
Given, u1 = u2 = u, θ1 = 60° , θ2 = 30°
In 1st case, we know that rangeR1 = u2 sin 2(60°) = u2 sin 120° g g = u2 sin(90° + 30°) g = u2 (cos 30°) = √3 u2 g 2g
In 2nd case, when θ2 = 30° , thenR2 = u2 sin 60° = √3 u2 ⇒ R1 = R2 g 2g
[we get same value of ranges].
- For angles of projection of a projectile (45° – θ) and (45° + θ), the horizontal ranges described by the projectile are in the ratio of
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(45° – θ) & (45° + θ) are complementary angles as 45° – θ + 45° + θ = 90° . We know that if angle of projection of two projectiles make complementary angles, their ranges are equal. In this case also, the range will be same. So the ratio is 1 : 1.
Correct Option: D
(45° – θ) & (45° + θ) are complementary angles as 45° – θ + 45° + θ = 90° . We know that if angle of projection of two projectiles make complementary angles, their ranges are equal. In this case also, the range will be same. So the ratio is 1 : 1.
