Question

In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot for 0.0342 s, during which time it experiences an acceleration of 186 m/s2. The ball is launched at an angle of 45.9 ° above the ground. Determine the (a) horizontal and (b) vertical components of the launch velocity.

Answer 1

The horizontal and vertical components of the launch velocity can be calculated by first determining the total change in velocity using the formula Δv = a * t, and then using trigonometric functions with the given angle to separate this velocity into its horizontal (cosine function) and vertical (sine function) components.

Step-by-step explanation:

To find the horizontal and vertical components of the launch velocity when a kicker attempts a field goal, we use the given acceleration and time of contact. The total change in velocity (Δv) during the kick can be calculated using the formula Δv = a * t, where 'a' represents the acceleration and 't' the time.

First, we calculate the total change in velocity:

Δv = 186 m/s2 * 0.0342 s = 6.36 m/s

This is the total velocity gained by the ball when kicked. Now, we need to break down this velocity into its horizontal and vertical components by using the launch angle (θ).

(a) The horizontal component (vx) is: vx = Δv * cos(θ)

(b) The vertical component (vy) is: vy = Δv * sin(θ)

For this problem, θ = 45.9°. Therefore:

(a) vx = 6.36 m/s * cos(45.9°)

(b) vy = 6.36 m/s * sin(45.9°)

The horizontal and vertical components of the launch velocity can now be calculated using a calculator to compute the trigonometric functions.

Answer 2

b) v_y = 4.57 m / s

a) vₓ = 4.43 m / s

Step-by-step explanation:

This is an exercise in kinematics, where we assume that the acceleration is in the direction of the force and the initial body with zero velocity

v = v₀ + a t

v = 0 + a t

v = 186 0.0342

v = 6.36 m / s

let's use trigonometry to decompose this velocity

sin 45.9 = v_y / v

cos 45.9 = vₓ / v

v_y = v sin 45.9

vₓ = v cos 45.9

v_y = 6.36 sin 45.9

vₓ = 6.36 cos 45.9

v_y = 4.57 m / s

vₓ = 4.43 m / s

ₓ