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=‌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∕ sAngle of projection,
θ=30∘Substituting these values into the formula:
H1=‌| (10)2sin‌2(30∘) |
| 2×9.8 |
We know that
sin‌(30∘)=‌, so:
H1=‌=‌=‌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∘)=‌, so:
H2=‌=‌=‌ Now, to find the ratio of the maximum heights, we calculate:
Ratio
=‌=‌=‌=‌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