a quarterback throws a pass to a receiver. the release point for the football is 1.8 m above the ground. he projects the ball with a speed of 20 m/s at an angle of 40 above the horizontal. If the pass falls incomplete, how long is it in the air? If the pass falls incomplete, how fat from the quarterback does it land? How high above the release point will the ball reach? A receiver 15 m from the quarterback is running at a constant speed away from him at the time of the release. how fast must the receiver be runnimg to be able to catch the ball, assuming he receives it at ground level(makes a diving catch)?
To find the answers to these questions, we can use the principles of projectile motion. Let's break down the problem step by step:
1. Find the time of flight (how long the pass is in the air):
The time of flight can be found using the vertical component of the motion. The formula to calculate the time of flight is given by:
Time of flight (t) = 2 * (initial vertical velocity) / (acceleration due to gravity)
In this case, the initial vertical velocity can be calculated using the initial velocity and the launch angle. Given that the initial velocity is 20 m/s, and the launch angle is 40 degrees, we can use:
Initial vertical velocity (Vy) = initial velocity (v) * sin(launch angle)
With the value of Vy, we can now calculate the time of flight using the formula mentioned above.
2. Find the horizontal distance traveled:
The horizontal distance traveled can be found using the horizontal component of the motion. The formula to calculate the horizontal distance is given by:
Horizontal distance (d) = initial horizontal velocity * time of flight
The initial horizontal velocity can be calculated using the initial velocity and the launch angle. Given that the initial velocity is 20 m/s, and the launch angle is 40 degrees, we can use:
Initial horizontal velocity (Vx) = initial velocity (v) * cos(launch angle)
With the value of Vx and the time of flight from step 1, we can now calculate the horizontal distance traveled.
3. Find the maximum height reached:
The maximum height reached is the vertical position at the peak of the projectile's trajectory. To find this, we need to calculate the time it takes for the projectile to reach its maximum height (t_peak). The formula for t_peak is given by:
t_peak = (initial vertical velocity) / (acceleration due to gravity)
With the value of t_peak, we can substitute it back into the vertical motion equation to find the maximum height (H):
H = (initial vertical velocity)^2 / (2 * acceleration due to gravity)
4. Find the receiver's required speed:
Now, to find the receiver's required speed to catch the ball at ground level, we need to consider the horizontal distance traveled and the time of flight. Given that the receiver is 15 meters away from the quarterback and the time of flight is known from step 1, we can now calculate the receiver's required speed. The formula to calculate the receiver's speed is given by:
Receiver's speed = horizontal distance / time of flight
By plugging in the values obtained from previous steps, we can now find the receiver's required speed.
I hope this breakdown helps you understand the problem-solving approach. Now you can use the given values to calculate the answers to each of the questions step by step.