A quarterback throws a football toward a receiver with an initial speed of 21 m/s at an angle of 30° above the horizontal. At that instant, the receiver is 12 m from the quarterback. In what direction and with what constant speed should the receiver run in order to catch the football at the level at which it was thrown?

Question

A quarterback throws a football toward a receiver with an initial speed of 21 m/s at an angle of 30° above the horizontal. At that instant, the receiver is 12 m from the quarterback. In what direction and with what constant speed should the receiver run in order to catch the football at the level at which it was thrown?

Choose one:
a. The receiver should run in the direction the football is traveling.
b. The receiver should run in the direction opposite to that in which the football is travelling

what constant speed should the receiver run in order to catch the football at the level at which it was thrown?

Answer 1

Using d = (V^2/g)sin2µ

the distance the football travels derives from d = (21^2/9.8)sin(60) = 38.97 m.

The time it will take the ball to reach the receivers hands derives from Vf = Vo - gt or 0 = 21sin60 - 9.8t making t = 1.85 sec.

Consequently, the receiver should run away from the quarterback at a speed of (38.97 - 12)/1.85 = 14.58m/s.

Answer 2

To determine the direction in which the receiver should run to catch the football, we need to consider the components of the initial velocity of the football. The velocity can be broken down into horizontal and vertical components.

Given:
Initial speed (v) = 21 m/s
Launch angle (θ) = 30°
Distance between the quarterback and receiver (d) = 12 m

The horizontal component of the velocity (v_x) remains constant throughout the motion. It can be calculated using the formula:
v_x = v * cos(θ)

In this case, v_x = 21 m/s * cos(30°) = 21 m/s * √3/2 = 21√3/2 ≈ 18.2 m/s

Since the receiver is 12 m away from the quarterback, they need to run at a speed that matches the horizontal component of the football's velocity (v_x) in order to catch it at the level it was thrown. So, the receiver should run at a constant speed of 18.2 m/s.

Now let's determine the direction in which the receiver should run. Since the horizontal component of the velocity remains constant, the receiver should run in the same direction as the football to match its horizontal motion. Therefore, the correct answer is:

a. The receiver should run in the direction the football is traveling.