Question

A ball of mass 0.4 kg is initially at rest on the ground. It is kicked and leaves the kicker's foot with a speed of 5.0 m/s in a direction 60° above the horizontal. The magnitude of the impulse imparted by the ball to the foot is most nearly:. ||J|| = 1. ||J|| = 1Ns.
2. ||J|| =(2/√3) Ns.
3. ||J|| = 2Ns.
4. ||J|| = 4Ns.
5. ||J|| = √3 Ns.

Answer 1

Answer:

the answer the correct  is 3

Explanation:

Let's use the relationship between momentum and momentum

         I = Δp

         I = m $v_{f}$ - m v₀

     

Let's calculate

         I = 0.4 5.0 - 0

         I = 2.0 N s

By Newton's law of action and reaction the force on the ball is equal to the force that the ball exerts on the foot, therefore the impulse on the foot of equal magnitude, but in the opposite direction

        I = 2.0 Ns with 60°

When reviewing the answer the correct  is 3

Answer 2

The magnitude of the impulse imparted by the ball to the foot is most nearly equal to 1 Ns. Hence, option (1) is correct.

Given data:

The mass of ball is, m = 0.4 kg.

The speed of ball is, v = 5.0 m/s.

And the angle of inclination with horizontal is, $\theta = 60^{\circ}$.

According to impulse-momentum concept, the force acting on an object for a short interval of time is equal to the change in momentum.

$I = \Delta p$

Here, I is the impulse.

Solving as,

$I = \Delta p\\I = mv - mu\\I = 0.4 \times 5 - m \times 0\\I = 2 \;\rm N-s$

Now, as per the Newton's law the force on the ball is equal to the force that the ball exerts on the foot, therefore the impulse on the foot of equal magnitude, but in the opposite direction. So,

$I'= I cos \theta\\\\I'= 2 \times cos60\\\\I' = 1 \;\rm N-s$

Thus, we can conclude that the magnitude of the impulse imparted by the ball to the foot is most nearly equal to 1 Ns. Hence, option (1) is correct.

Learn more about the impulse-momentum concept here:

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