If the initial velocity in horizontal direction of a projectile is unit vector î and the equation of trajectory is y = 5x(1 - x). The y component vector of the initial velocity i s_______ ĵ. (Take g = 10 m/s²)
Physics · Kinematics part-2 Projectile Motion · Motion in 2-D and ground to ground projectile
JEE Advanced 2022

Question

If the initial velocity in horizontal direction of a projectile is unit vector î and the equation of trajectory is y = 5x(1 - x). The y component vector of the initial velocity i s_______ ĵ. (Take g = 10 m/s²)

Physics · Kinematics part-2 Projectile Motion · Motion in 2-D and ground to ground projectile

JEE Advanced 2022

G1 Physics · Accepted Answer

The projectile trajectory is y = (uᵧ/uₓ)x - gx²/(2uₓ²). Here uₓ = 1 m/s and y = 5x - 5x². Comparing coefficients gives uᵧ/uₓ = 5, hence uᵧ = 5 m/s. Therefore the y-component vector is 5ĵ.