Question

Aaron Rodgers throws a football at 20.0 m/s to his wide receiver, who is running straight down the field at 9.4 m/s. If Aaron throws the football when the wide receiver is 10.0 m in front of him, (a) at what angle does Aaron have to launch the ball so the ball will be at the same height as the receiver when the receiver makes it to 20.0 m in front of Aaron? (b) Will the receiver be able to catch the ball?

a) 29.7°, Yes
b) 35.2°, Yes
c) 41.0°, No
d) 48.6°, No

Answer 1

To find the angle at which Aaron needs to launch the ball, we can use the concepts of projectile motion. The ball needs to be launched at an angle of approximately 29.7° to be at the same height as the receiver when the receiver makes it to 20.0 m in front of Aaron. It is possible for the receiver to catch the ball.

Step-by-step explanation:

To find the angle at which Aaron needs to launch the ball, we can use the concepts of projectile motion. The horizontal distance traveled by the receiver is 20.0 m, which is the same distance the ball needs to cover. The vertical distance traveled by the receiver is 0 m, since the receiver is at the same height when he reaches 20.0 m in front of Aaron.

Using the formulas for horizontal and vertical components of velocity, we can set up the following equations:

Horizontal component: vx = v * cos(θ)

Vertical component: vy = v * sin(θ)

Given that the receiver's speed is 9.4 m/s and the ball's initial speed is 20.0 m/s, we can set up the following equation: 9.4 = 20.0 * sin(θ)

Solving for θ, we find that θ ≈ 29.7°. Therefore, Aaron needs to launch the ball at an angle of approximately 29.7°.

Since the ball will be at the same height as the receiver when the receiver makes it to 20.0 m in front of Aaron, it is possible for the receiver to catch the ball. The correct answer is (a) 29.7°, Yes.