Question

A football quarterback is moving straight backward at a speed of$\mathbf{2}\mathbf{.}\mathbf{00}$m/s when he throws a pass to a player$\mathbf{18}\mathbf{.}\mathbf{0}$m straight downfield. The ball is thrown at an angle of role="math" localid="1668669019911" ${\mathbf{25}}^{\mathbf{o}}$relative to the ground and is caught at the same height as it is released. What is the initial velocity of the ball relative to the quarterback?

Short answer

The velocity of the ball relative to the quarterback is 17.2 m/s.

Step-by-step solution

Definition of velocity

The directional speed of an item in motion is an indication of its rate of change in position, as seen from a specific point of view and measured by a specific time standard

Stating given data

The speed of the football moving backward is $-2$m/s.

The quarterback will release the ball at angle of ${25}^o$.

The distance travelled by the ball is$18.0$ m.

Calculating initial velocity of ball relative to quarterback

The initial velocity of the ball relative to the Earth

$$\begin{gathered} R_x=\frac{{V_i}^2\sin 2\theta }{g} \\ 18=\frac{{\left(V_i\right)}^2\sin 2\left(25\right)}{9.8} \\ {V_i}^2=231 \\ {V}_i=15.2m/s \end{gathered}$$

The velocity of the ball relative to earth is $15.2$m/s.

The velocity of the ball relative to quarterback

$$\begin{gathered} V_{bq}=V_{be}+V_{eq} \\ {V}_{bq}=15.2+\left(2\right)..........[V_{eq}=V_{qe}] \\ {V}_{bq}=17.2m/s \end{gathered}$$

Hence the velocity of the ball relative to the quarterback is $17.2m/s$.