Question

A football is kicked at ground level with a speed of 25 m/s at an angle of 45 degrees to the horizontal. How far down field does it go (assume takeoff and landing at the same height)?

Answer 1

Let us consider the upwards direction as positive and the downwards direction as negative.

Gravitational acceleration = g = -9.81 m/s²

Initial velocity of the football = V = 25 m/s

Angle at which the football is kicked = = 45^o

Initial horizontal velocity of the football = V_x = VCos = (25)Cos(45) = 17.68 m/s

Initial vertical velocity of the football = V_y = VSin = (25)Sin(45) = 17.68 m/s

Time taken by the ball to reach the ground again = T

The takeoff and landing of the football are at the same height therefore the vertical displacement of the football is zero.

0 = V_yT + gT²/2

0 = V_y + gT/2

0 = 17.68 + (-9.81)T/2

T = 3.604 sec

Horizontal distance covered by the football = R

There is no horizontal force acting on the football therefore the horizontal velocity of the football is zero.

R = V_xT

R = (17.68)(3.604)

R = 63.7 m

Distance the football goes down field = 63.7 m