A player kicks a ball at an angle of 37 with the horizontal and with the initial velocity of 14.6m/s. A second player standing at a distance of 30.5m from the first in the direction of the kick starts running to meet the ball at the instant it is kicked. How fast must he run in order to catch the ball before it hits the ground? Pls show the workings
A player kicks a ball at an angle of 37 with the horizontal and with the initial velocity of 14.6m/s. A second player standing at a distance of 30.5m from the first in the direction of the kick starts running to meet the ball at the instant it is kicked. How fast must he run in order to catch the ball before it hits the ground? Pls show the workings
first find out the time of flight then distance betn ball and 2nd player then use speed formula
first find out the time of flight then distance betn ball and 2nd player then use speed formula
Response
Response
To solve this problem, we need to analyze the motion of the ball and the player separately and find the conditions for the player to catch the ball before it hits the ground.
First, we need to determine the time it takes for the ball to hit the ground. To do this, we can use the vertical motion of the ball, assuming there is no air resistance.
1. Find the vertical component of the initial velocity:
Vy = V * sin(θ)
= 14.6 * sin(37°)
= 8.76 m/s
2. Use the kinematic equation to find the time of flight (time for the ball to hit the ground):
y = (Vy * t) + (0.5 * g * t^2)
0 = (8.76 * t) - (4.9 * t^2)
This is a quadratic equation, so we can solve it by factoring or using the quadratic formula. By solving the equation, we find that t ≈ 1.78 seconds.
Now, we know that the player must reach the ball before this time, so let's analyze the horizontal motion of the player.
3. We need to find the horizontal component of the initial velocity of the ball:
Vx = V * cos(θ)
= 14.6 * cos(37°)
= 11.61 m/s
4. Find the distance the player needs to cover to reach the ball before it hits the ground. This distance is equal to the initial horizontal distance between the players, which is 30.5 m.
5. Use the formula for uniform motion (distance = speed * time) to find the required speed of the player:
Speed = Distance / Time
= 30.5 / 1.78
≈ 17.15 m/s (rounded to two decimal places)
Therefore, the second player must run at a speed of approximately 17.15 m/s to catch the ball before it hits the ground.
Please note that this solution assumes ideal conditions without considering factors like air resistance or the size of the ball.
t = vo sinθ / ½ g
x = vo cosθ t
so he has t seconds to run x meters