football is kicked off with an initial speed of 66 ft/s at a projection angle of 45 degrees. A receiver on the goal line 63 yd away in the direction of the kick starts running to meet the ball at that instant. What must be his minimum speed (in feet/second) if he is to catch the ball before it hits the ground?
I found the x and y velocity's to be
66cos45=46.669 and 66sin45=46.669 and then solved for time using the y velocity by using Y=Yo+VoT+1/2(a)(t^2)
0=0+46.669-16.085t^2
t(46.669-16.085t)
t=0 and t=2.9sec
After this im not really sure what to solve for next.
apparently the ball hits the ground in 2.9 seconds. The horizontal speed of the ball is 66*.707 = 46.67 ft/s, so in those 2.9 seconds the ball travels
46.67*2.9 = 135.34 ft
The runner starts 63*3 = 189 feet away, so he must run 53.66 ft in 2.9 seconds, or 18.5 ft/s
To determine the minimum speed the receiver must have to catch the ball before it hits the ground, we need to consider the horizontal distance covered by the ball and the time it takes for the ball to reach that distance.
From your calculations, you have correctly determined the time it takes for the ball to reach the ground as 2.9 seconds.
Next, we need to find the horizontal distance covered by the ball in 2.9 seconds. Since the initial velocity of the ball in the x-direction is 46.669 ft/s, we can calculate this distance using the equation:
horizontal distance = initial velocity * time
horizontal distance = 46.669 ft/s * 2.9 s
horizontal distance = 135.0031 ft
Now, we need to find the time it takes for the receiver to reach the same horizontal distance. We know that the receiver starts running at the same instant the ball is kicked. Let's assume the receiver's speed is "v" ft/s.
Since the horizontal distance covered by the receiver is the same as the ball and the time taken is the same, we can set up the equation:
horizontal distance = receiver's speed * time
135.0031 ft = v ft/s * 2.9 s
Now, we can solve this equation to find the minimum speed (v) required for the receiver to catch the ball before it hits the ground.
v = 135.0031 ft / 2.9 s
v ≈ 46.55 ft/s
Therefore, the receiver must have a minimum speed of approximately 46.55 ft/s to catch the ball before it hits the ground.