A player kicks a football at an angle of 45 degree with initial speed of 20 metre per second a second player on the goal line 60 metre away in the direction of a kick start training to receive the ball at that instant find the constant speed of the second player with which he should run to catch the ball before he hit the ground

To find the constant speed at which the second player should run to catch the ball before it hits the ground, we need to consider the horizontal and vertical components of the ball's motion separately.

Let's start by finding the time it takes for the ball to reach the ground. We can use the vertical component of the ball's motion for this calculation. The equation that relates the vertical displacement (distance) and the initial vertical velocity of the ball is:

y = Viy * t + (1/2) * g * t^2

Here, y represents the vertical displacement (which is the negative of the initial height of the ball), Viy is the initial vertical velocity (which is the initial speed multiplied by the sine of the launch angle, as the angle is measured from the horizontal), t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Since the ball hits the ground when y = 0, we can solve the equation for t:

0 = Viy * t + (1/2) * g * t^2

Now, let's find the horizontal component of the ball's motion. The equation relating horizontal displacement and initial horizontal velocity is:

x = Vix * t

Here, x represents the horizontal displacement, Vix is the initial horizontal velocity (which is the initial speed multiplied by the cosine of the launch angle).

Since the second player is positioned 60 meters away from the kicker in the direction of the kick, the time taken for the ball to travel this horizontal distance is 60 meters. Therefore, we have:

60 = Vix * t

Now we can solve for t using this equation and substitute it into the equation for y:

60 = Vix * (0 = Viy * t + (1/2) * g * t^2)

Since the initial speed of the ball is 20 m/s and the launch angle is 45 degrees, we can calculate the initial horizontal and vertical velocities:

Vix = 20 * cos(45)
Viy = 20 * sin(45)

Substituting these values into the equation:

60 = (20 * cos(45)) * (0 = (20 * sin(45)) * t + (1/2) * g * t^2)

Now we can solve this equation to find the time it takes for the ball to hit the ground:

60 = (20 * cos(45)) * (0 = (20 * sin(45)) * t + (1/2) * g * t^2)

Simplify the equation:

60 = (20 * cos(45)) * (0 = 9.8 * t + (1/2) * 9.8 * t^2)

Multiplying out the terms:

60 = (20 * cos(45)) * (9.8 * t + (1/2) * 9.8 * t^2)

Now we can solve this quadratic equation to find the value of t:

(20 * cos(45)) * (9.8 * t + (1/2) * 9.8 * t^2) = 60

After finding the value of t, we can use it to find the speed at which the second player should run to catch the ball. The distance covered by the second player is 60 meters, and the time taken is t. Therefore, the required constant speed is:

Speed = Distance / Time = 60 / t

Now, you can substitute this value of t into the equation for the speed to find the constant speed at which the second player should run to catch the ball before it hits the ground.

4.9 t = 20sin45

x = t* 20cos45
2nd player must go 60 - x in the same amount of time you found.