A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity v/2 from the top of the tower of height 4H will touch the ground at a distance o f ______ m.
Physics · Kinematics part-2 Projectile Motion · Projectile from height
JEE Mains 2024 08 Apr Evening Shift

Question

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity v/2 from the top of the tower of height 4H will touch the ground at a distance o f ______ m.

Physics · Kinematics part-2 Projectile Motion · Projectile from height

JEE Mains 2024 08 Apr Evening Shift

G1 Physics · Accepted Answer

For first projectile: Time of flight: t₁ = √(2H/g) Horizontal range: 100 = v√(2H/g) For second projectile: Height = 4H Horizontal speed = v/2 Time of flight: t₂ = √[2(4H)/g] = 2√(2H/g) Horizontal range: x = (v/2)t₂ = (v/2)[2√(2H/g)] = v√(2H/g) = 100 m