Answer to Question #177174 in Classical Mechanics for Joseph Se

Question

The final answer should be in the format of "tolerance of ± in the third significant digit.

1.The drag racer P starts from rest at the start line S and then accelerates along the track. When it has traveled 102 m, its speed is 51 m/s. For that instant, determine the values of r˙ and θ˙ relative to axes fixed to an observer O in the grandstand G as shown.

28 meters from point O ( it is the base of the triangle)

r˙ = ___ m/s

θ˙ = ____ rad/s

Answer 1

Given,

At a distance of 102m, speed = 51 m/s

Angle with the horizontal $=\theta$

Distance between O and S = 28m

Initial velocity = 0

$v=u+at$

$at= 51$

$\Rightarrow \overrightarrow{r}= -102\hat{i}+28\hat{j}$

$\Rightarrow |\overrightarrow{r}|=\sqrt{(-102)^2+(28)^2}$

$\Rightarrow|\overrightarrow{r}|=105.77$

$\tan(\theta)=\frac{28}{102}$

$\Rightarrow \theta=\tan^{-1}(\frac{28}{102})$

$\Rightarrow \theta = 15.35^\circ$