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

Solution

Physics sir · 3 steps

Write the trajectory in terms of uₓ and u_y, then match coefficients with 5x - 5x².

1. Trajectory with components. Horizontal motion gives x = uₓ t, so t = x/uₓ. Put this into y = u_y t - 1/2gt².

   y = u_y/uₓ x - g/2uₓ² x²

2. Match coefficients. The given path is y = 5x - 5x². Comparing the x terms gives u_y/uₓ = 5. As a check, the x² term gives g/2uₓ² = 10/(2 × 1²) = 5, which agrees with uₓ = 1 m s⁻¹.
3. So. u_y = 5 × uₓ = 5 × 1 = 5 m s⁻¹, so the vertical component is 5 ĵ.

The idea to keep. For any projectile, the coefficient of x in the trajectory is u_y/uₓ and the coefficient of x² is g/2uₓ². Match terms and you read off the components directly.

Answer from the NTA final answer key. Solution by PrepWiser.