During a football game, the quarterback throws the ball to...

Name: Problem 34, Chapter 8: Geometry A Common Core Curriculum
Uploaded: 2019-09-06T10:18:29-08:00
Duration: 3 min 58 s
Channel: Steven Swee
Description: During a football game, the quarterback throws the ball to the receiver. The receiver is between two defensive players, as shown. If Player 1 is closer to the quarterback when the ball is thrown and both defensive players move at the same speed, which player will reach the receiver first? Explain your reasoning.

During a football game, the quarterback throws the ball to the receiver. The receiver is between two defensive players, as shown. If Player 1 is closer to the quarterback when the ball is thrown and both defensive players move at the same speed, which player will reach the receiver first? Explain your reasoning.

Key Concepts

Relative Distance

This concept refers to the measure of space between two points. In motion problems, an object that starts closer to the target has less distance to cover, making it a critical factor in determining which moving object arrives first when speeds are equal.

Constant Speed

Constant speed implies that an object covers equal amounts of distance in equal intervals of time. When multiple objects move at the same constant speed, the one with a shorter distance to travel will naturally reach the destination sooner.

Time-Distance Relationship

This principle, expressed mathematically as time being equal to distance divided by speed, is key in analyzing motion. In scenarios where two objects move at the same speed, comparing their respective distances to the target allows us to determine which object will take less time to arrive.

Transcript

00:01 So for this problem, we have a scenario in an american football game.

00:06 And we're given that player one is closer to the quarterback than player two.

00:12 And we're finding that, assuming that both players run at the same speed, which player gets to the receiver first.

00:18 So the quarterback, there was a football to the receiver.

00:23 We're asked to figure out who reaches the receiver first, player one and player two.

00:28 And we're assuming that the speed, that players one and players two run at is the same.

00:36 So when the speed's the same, to reach a certain point, depend how fast you reach a certain point or how much time it takes to reach a certain point depends only on distance.

00:48 So for here, we're assuming that the closer you are to the receiver, you're going to reach there first.

00:57 So it would be helpful to make some labels.

01:01 So let's denote the length from a line segment from player one to the quarterback as a1 and i'm playing one to the receiver as b1 and quarterback to the player two as a2 and from player to the receiver as b2.

01:22 Now, how do we figure this out? well, one thing i notice here is that we have these two angles.

01:30 So we're right these two angles, and the recoval to one level.

01:34 This means that the line segment from the quarterback to the receiver bisects this angle in the triangle, from player one quarterback to player two, this big triangle...

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