A player kicks a football at an angle of 45° with an initial speed of 20 m/s. A second player on the goal line 60 m away in the direction of the kick starts running to receive the ball at ground level. Find the speed with which he should run to catch the ball before it hits the ground. Take g = 10 m/s².
Physics · Kinematics part-2 Projectile Motion · Motion in 2-D and ground to ground projectile
JEE Mains NEET

Question

A player kicks a football at an angle of 45° with an initial speed of 20 m/s. A second player on the goal line 60 m away in the direction of the kick starts running to receive the ball at ground level. Find the speed with which he should run to catch the ball before it hits the ground. Take g = 10 m/s².

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

G1 Physics · Accepted Answer

For u = 20 m/s and θ = 45°, the time of flight is T = 2u sin45°/g = 2√2 s and the range is R = u²/g = 40 m. The second player starts 60 m from the kicker, so he must run 60 - 40 = 20 m toward the kicker in time 2√2 s. Required speed = 20/(2√2) = 5√2 ≈ 7.07 m/s.