Question

A projectile is fired straight upward from earth's surface with a speed that is half the escape speed. if r is the radius of earth, the highest altitude reached, measured from the surface, is?

Answer 1

A projectile is fired straight upward from earth's surface with a speed that is half the escape speed. if r is the radius of earth, the highest altitude reached, measured from the surface, is

                                                                  h= $\frac{R}{1-k^{2} }$

At maximum height h, KE of the projectile will be zero.

Using conservation of energy, $KE_{i} +PE_{i}=KE_{f}+PE_{f}$

or,

          $\frac{1}{2}m(kv)^{2} -\frac{GMm}{R}=0-\frac{GMn}{H}$

or,

           $\frac{1}{2}(k)^{2}(2gR) -\frac{GMm}{R}+\frac{GM}{H}=0$

where escape velocity is $\sqrt{2gR}$

           gR$k^{2}$ -  gR  +  g$h^{2}$/H=0

where

             $g=\frac{GM}{R^{2} }$

​or,

             $k^{2} -1 +\frac{R}{H}= 0$

               H=   $\frac{R}{1-k^{2} }$

To learn more about Projectile motion

brainly.com/question/11049671

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