Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.

An eagle goes straight up with an initial velocity of 75m/s toward its food. Its food is located 250m above the ground. How fast will the eagle be moving when she reaches her food?

Sagot :

The vertical distance covered by the eagle can be given as,

[tex]h=ut+\frac{1}{2}gt^2[/tex]

Plug in the known values,

[tex]\begin{gathered} 250m=(75\text{ m/s)t+}\frac{1}{2}(-9.8m/s^2)t^2 \\ -(4.90ms^{-2})t^2+(75\text{ m/s)t-250m=0} \\ (4.90ms^{-2})t^2-(75\text{ m/s)t+250 m=0} \end{gathered}[/tex]

The above equation can be further solved as,

[tex]\begin{gathered} t=\frac{75\text{ m/s}\pm\sqrt[]{(75m/s)^2-4(4.90ms^{-2})(250\text{ m)}}}{2(4.90ms^{-2})^{}} \\ =\frac{75\text{ m/s}\pm26.9\text{ m/s}}{9.80m/s^2} \\ =10.4\text{ s, }4.91\text{ s} \end{gathered}[/tex]

Therefore, the time taken by eagle to reach at food is 10.4 s or 4.91 s.