Question

On the putting green, a golf ball travels at 1.2 m/s in a direction of 150°. The ball encounters wind blowing at 1.3 m/s in the direction of 50°. What is the true speed and direction of the ball? Round the speed to the thousandths place and direction to the nearest degree.

Answer 1

Given:

The speed of the golf ball is v = 1.2 m/s in the direction of 150 degrees.

The wind speed is 1.3 m/s in the direction of 50 degrees.

To find the true speed and direction of the ball.

Explanation:

The information can be drawn as

Here, the blue vector shows the golf direction.

The red vector shows the wind direction.

The true speed in the x-direction will be

$\begin{gathered} v_x=\text{ 1.2cos\lparen30}^{\circ}\text{\rparen-1.3cos\lparen50}^{\circ}\text{\rparen} \\ =\text{ 0.204 m/s} \end{gathered}$

The true speed in the y-direction will be

$\begin{gathered} v_y=1.2sin(30^{\circ})-1.3sin(50^{\circ}) \\ =-0.396\text{ m/s} \end{gathered}$

The true speed will be

$\begin{gathered} v=\sqrt{(v_x)^2+(v_y)^2}^ \\ =\sqrt{(0.204)^2+(0.396)^2} \\ =0.445\text{ m/s} \end{gathered}$

The direction of speed will be

$\begin{gathered} \theta=tan^{-1}(\frac{v_y}{v_x}) \\ =tan^{-1}(\frac{0.396}{0.204}) \\ =62.7^{\circ} \end{gathered}$