BITSAT 2024 Shift 1 Paper

When a projectile is launched with a velocity of 40m∕ s at an angle θ to the horizontal, and its inclination with the horizontal becomes zero after t seconds, we want to determine the value of cot θ.
Maximum Height Condition: The projectile's inclination with the horizontal becomes zero at its maximum height.
Time to Reach Maximum Height:
t=‌

usin‌θ

g

Solving for u, we get:
u=‌

gt

sin‌θ

Horizontal Range R :
R=u‌cos‌θ×(2t)
Solving for cos‌θ :
cos‌θ=‌

R

2ut

Substituting u from (i):
cos‌θ=‌

R

2⋅‌ gt sin‌θ ⋅t

Simplifying gives:
cos‌θ=‌

Rsin‌θ

2gt2

Finding cot‌θ :
cot‌θ=‌

cos‌θ

sin‌θ

=‌

R

2gt2

Substituting g=10m∕ s2 :
cot‌θ=‌

R

2×10t2

=‌

R

20t2