Q147 / 180 · COMEDK 2026 (9 May Shift 2) · Physics
A boy, standing at a certain height, kicks a football horizontally with a velocity of $19.6\ ms^{-1}$. What will be the ratio of horizontal and vertical components of velocities after 2s?
- Correct answerA$1:1$
- B$\left(\dfrac{\sqrt{3}}{2}\right):1$
- C$1:\sqrt{2}$
- D$1:0.5$
Solution
Initial horizontal velocity, $u_x = 19.6\ ms^{-1}$
Initial vertical velocity, $u_y = 0\ ms^{-1}$
Acceleration in horizontal direction, $a_x = 0$
Acceleration in vertical direction, $a_y = g = 9.8\ ms^{-2}$
Time, $t = 2\ s$
Horizontal velocity after $2\ s$, $v_x = u_x + a_x t = 19.6\ ms^{-1}$
Vertical velocity after $2\ s$, $v_y = u_y + a_y t = 0 + 9.8 \times 2 = 19.6\ ms^{-1}$
Ratio of horizontal and vertical components of velocities $= \dfrac{v_x}{v_y} = \dfrac{19.6}{19.6} = 1:1$
Answer: $1:1$
Initial vertical velocity, $u_y = 0\ ms^{-1}$
Acceleration in horizontal direction, $a_x = 0$
Acceleration in vertical direction, $a_y = g = 9.8\ ms^{-2}$
Time, $t = 2\ s$
Horizontal velocity after $2\ s$, $v_x = u_x + a_x t = 19.6\ ms^{-1}$
Vertical velocity after $2\ s$, $v_y = u_y + a_y t = 0 + 9.8 \times 2 = 19.6\ ms^{-1}$
Ratio of horizontal and vertical components of velocities $= \dfrac{v_x}{v_y} = \dfrac{19.6}{19.6} = 1:1$
Answer: $1:1$
Hence, the correct answer is option: 'A'.