COMEDK 2024 Shift 1 Paper

To determine the ratio of the maximum heights attained in the two cases, let's start by deriving the formula for the maximum height reached by a projectile. The maximum height H for a projectile is given by:
H=‌

u2sin‌2(θ)

2g

Here:
u is the initial velocity
θ is the angle of projection g is the acceleration due to gravity
For the first case:
Initial velocity, u=10m∕ s
Angle of projection, θ=30∘
Substituting these values into the formula:

H1=‌

(10)2sin‌2(30∘)

2×9.8

We know that sin‌(30∘)=‌

1

2

, so:
H1=‌

100( 1 2 )2

2×9.8

=‌

100× 1 4

2×9.8

=‌

25

19.6

For the second case, the mass and the angle of projection are doubled, but the mass does not affect the height. Therefore, the new angle of projection is:
θ′=2×30∘=60∘
Using the same initial velocity u=10m∕ s, we substitute into the formula:
H2=‌

(10)2sin‌2(60∘)

2×9.8

We know that sin‌(60∘)=‌

√3

2

, so:
H2=‌

100( √3 2 )2

2×9.8

=‌

100× 3 4

2×9.8

=‌

75

19.6

Now, to find the ratio of the maximum heights, we calculate:
Ratio =‌

H1

H2

=‌

‌ 25 19.6

19.6

=‌

25

75

=‌

1

3

Therefore, the ratio of the maximum height attained in the former to the latter case is 1:3, which corresponds to Option C.
Option C: 1:3