91影视

Speed of albatross is$15m/s$

$h=2.0m$

$胃=30掳$

Speed of hawk is$15m/s$

Speed of hawk鈥檚 shadow on the wall is$45m/s$

As the sun is far away, we consider that the rays coming from the sun are parallel, i.e., the angle between the sunray and the bird鈥檚 position is the same everywhere.

Formula:

$\text{迟补苍鈥�}胃=y/x$

$v=\frac{dx}{dt}$

The rays coming from the sun are parallel. So, the angle formed by the sunrays with the bird at one position is the same as the one formed with the bird at another position.

Therefore, the shadow of the bird moves on the ground with the same speed as that of the bird.

Thus, the shadow of the albatross moves across the level ground with speed$15m/s$

Now the bird is in the position$x>0$from the wall. So, its shadow on the wall is at a distance$0鈮�y鈮�h$from the top of the wall.

From the figure,

$\begin{array}{c}\text{迟补苍鈥�}胃=\frac{y}{x}\\ y=x\text{tan}\text{鈥�}胃\end{array}$

Thus,

$\begin{array}{c}\frac{dy}{dt}=\frac{dx}{dt}\text{迟补苍鈥�}胃鈰�鈰�鈰�鈰�鈰�鈰�\left(1\right)\\ \frac{dy}{dt}=(鈭�15)\text{迟补苍鈥�}30掳\\ =(鈭�15)脳0.577\\ =-8.7m/s\end{array}$

This means that the distanceyi.e., the positive number downward from the top of the wall is shrinking at the rate of 8.7 m/s.

Thus, the speed at which the shadow of the albatross moves up the wall is.$8.7\text{鈥�}m/s$

$\text{迟补苍鈥�}胃$is directly proportional to the value of the $胃$in the range.$0掳<胃<90掳$

From equation (1), it is clear that the value of $\frac{dy}{dt}$is maximum when$\text{迟补苍鈥�}胃$ is maximum. Thus, the larger value of$\left|\frac{dy}{dt}\right|$ implies a larger value of.$胃$

Thus, we can conclude that the sun is higher in the sky when the hawk glides by.

$\frac{dy}{dt}=45m/s$

From equation (1), we have

$\begin{array}{c}\frac{dy}{dt}=\frac{dx}{dt}\text{迟补苍鈥�}胃\\ 45=\frac{dx}{dt}\text{迟补苍鈥�}胃\end{array}$

The speed of hawk is $\frac{dx}{dt}=15m/s$

Therefore,

$\begin{array}{c}45=15\text{鈥�}\text{tan}\text{鈥�}胃\\ \text{tan}\text{鈥�}胃=\frac{45}{15}\\ 胃=\left(71.56\right)掳\\ 鈮�\left(72\right)掳\end{array}$

The angleof the Sun if the speed of the hawk鈥檚 shadow on the wall is 45 m/s is$胃=72掳$