Q.A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is

Concept: Change in velocity (even at constant speed) requires a net force in the direction of $\Delta \vec{v}$.

The player's velocity changes from northward to westward while maintaining the same speed $v$. Represent the initial velocity as $\vec{v}_i = v\hat{j}$ (north) and final velocity as $\vec{v}_f = -v\hat{i}$ (west).

The change in velocity is:

This points south-west (equal components south and west), so the net force must also point south-west by Newton's second law. …

Why friction, and why south-west?

A change in velocity—even at constant speed—means acceleration. Newton's second law tells us the net force must point in the direction of that acceleration. When the player pivots from north to west, the velocity vector rotates through 90°. The acceleration during this turn does not point along the initial or final direction of motion; it points toward the center of the curve, which lies somewhere between south and east—that is, toward the south-west.

Now, what supplies this force? The player's muscles can only push against something. On ice, the skate blade pushes backward and sideways against the ice, and by Newton's third law the ice pushes forward and sideways on the skate. This reaction force from the ice is friction. Muscle forces are internal to the player's body; they reposition limbs and apply force to the skate, but the external force that accelerates the player's center of mass is the friction between skate and ice.

Step-by-step reasoning

1. Identify the velocity change. Initial velocity $\vec{v}_i$ points north; final velocity $\vec{v}_f$ points west. Both have the same magnitude $v$. The change in velocity is

In components (taking north as $+\hat{y}$ and east as $+\hat{x}$):

This vector points south-west (negative $x$ and negative $y$).

2. Find the direction of acceleration.

   Acceleration is $\vec{a} = \Delta\vec{v}/\Delta t$, so it points in the same direction as $\Delta\vec{v}$: south-west.

3. Apply Newton's second law.

   The net force is

which also points south-west. …

Concept: Force follows the direction of $\Delta \vec v$, and its physical origin is friction

Step 1: Set up a coordinate system.

Let $\hat i$ = east, $\hat j$ = north. Initial velocity $\vec v_i = v\hat j$

(north); final velocity $\vec v_f = -v\hat i$ (west); same speed $v$.

Step 2: Compute the change in velocity.

This has equal negative $x$ and $y$ components — it points south-west.

Step 3: Apply Newton's second law.

The net force is along $\Delta \vec v$ (since $\vec F = m\,\Delta\vec v/\Delta t$),

so the net force is directed south-west.

Step 4: Identify the physical agent. …