A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is $1000N$, the players have equal pulls, and the angle between the two ropes is $20°$. How hard must each player pull to drag the coach at a steady$2.0m/s$?

The force exerted on a mass that causes it to change velocity.

$1000N$is the friction force on the sled. $20°$is the angle between the two ropes and the players drag the sled with equal force at a steady speed of $2.0m/s$.

The free body diagram of the arrangement is shown:

Using Newton's second law, $\sum _{}{F}_x=ma$

where, mass of the player is $m$and acceleration of the player is $a$.

But, here the players drag the sled with constant steady speed of $2.0m/s$. So, the acceleration is zero as the rate of change of velocity is zero.

Substitute $0m/s^2$for $a$.

$$\begin{gathered} \sum _{}{F}_x=m\left(0m/s^2\right) \\ \sum _{}{F}_x=0 \end{gathered}$$

Resolving the components of forces in the ropes in x-direction,

$-F_f+2T\cos \theta =0$

The tension in the rope or the force at which the each player pull the rope is $T$.

The angle made by the rope with the sled is $\theta$.

The friction force is $F_f$.

Substitute $1000N$for $F_f$and $10°$for $\theta$.

$$\begin{gathered} -1000N+2T\cos 10°=0 \\ T=\frac{1000N}{2\cos 10°} \\ =507.71 \\ \approx 508N \end{gathered}$$

Hence, force required by each player to pull the rope is$508N$.