Question

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

• A. along south-west
• B. along eastward
• C. along northward
• D. along north-east

Answer 1

The Correct Option is D

When the football player moves southward and suddenly turns eastward with the same speed, a change in direction occurs, which constitutes an acceleration. According to Newton's Second Law of Motion, when there is acceleration, a net force must be acting on the player.

The force responsible for turning the player is the centripetal force, which always acts towards the center of the path's curvature. In this scenario, the player's initial velocity vector points southward, and the final velocity vector points eastward. These velocities form a right-angle triangle. 

The change in velocity, also known as the resultant velocity change, is represented by the vector pointing from the object's past to the new velocity vector. This vector can be determined using the vector subtraction method where:

Δv = v_final - v_initial

If 'v' is the speed, then:

• v_initial = -v ĵ (southward)
• v_final = v î (eastward)

Thus, the change in velocity Δv is:

Δv = vî - vĵ

This resultant velocity change vector points northeast, having components in both the north and east directions.

Therefore, the direction of the force acting on the player is:

Along north-east

Answer 2

The correct option is (D): along north-east
\(\vec{V}_i=V\)(southward)
\(\vec{V}_f=V\)(Eastward)
\(\vec{\Delta V} = \vec{V_f}-\vec{V_i}\)
= along north-east