91影视

The given data can be listed below,

• The velocity vector of the bird is,$\stackrel{鈫�}{v}=\left(伪-尾t^2\right)\hat{i}+纬t\hat{j}$
• The value of constants are,$伪=2.4m/s,尾=1.6m/s^3,纬=4.0m/s^2$

A reference source and a point or objects are separated by a distance known as altitude, which is often measured vertically or "up鈥� direction.

The position vector of bird is calculated by integrating the velocity vector which can be given by,

$\stackrel{鈫�}{r}={鈭�}_0^t\stackrel{鈫�}{v}\left(t\right)dt$

Substitute the value in the above,

role="math" localid="1664865082101" $$\begin{gathered} \stackrel{鈫�}{r}={鈭�}_0^t\left({\left(伪-尾t\right)}^2\hat{i}+纬t\hat{j}\right)dt \\ =\left(伪t-\frac{尾}{3}{t}^3\right)\hat{i}+\left(\frac{纬}{2}{t}^2\right)\hat{j} \end{gathered}$$

The acceleration of the bird is calculated by differentiating velocity vector with respect to time which can be given by,

$\stackrel{鈫�}{a}=\frac{d\stackrel{鈫�}{v}}{dt}$

Substitute values of velocity vector in the above,

$$\begin{gathered} \stackrel{鈫�}{a}=\frac{d\left(\left(伪-尾t^2\right)\hat{i}+纬t\hat{j}\right)}{dt} \\ =\left(-2尾t\right)\hat{i}+纬t\hat{j} \end{gathered}$$

Thus, the position and acceleration vector as function of time are$\left(伪t-\frac{尾}{3}{t}^3\right)\hat{i}+\left(\frac{纬}{2}{t}^2\right)\hat{j}$ and$\left(-2尾t\right)\hat{i}+纬t\hat{j}$ respectively.

The time at which the the horizontal component is zero is given by,

$$\begin{gathered} 伪t-\frac{尾}{3}{t}^3=0 \\ {t}^2=\frac{3伪}{尾} \end{gathered}$$

The altitude of bird is given by,

$y=\frac{纬}{2}{t}^2$

Substitute all the values in the above,

$$\begin{gathered} y=\frac{纬}{2}\left(\frac{3伪}{尾}\right) \\ =\frac{3\left(2.4m/s\right)\left(4m/s^2\right)}{2\left(\left(1.6m/s^3\right)\right)} \\ =9.0m \end{gathered}$$

Thus, the altitude of bird when it flies first time is 9.0 m