Q.43 - Excercises And Problems A projectile is shot straight up... [FREE SOLUTION]

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Chapter 13: Q.43 - Excercises And Problems (page 355)

A projectile is shot straight up from the earth鈥檚 surface at a speed of $10, 000 k m / h$ . How high does it go?

Short Answer

Expert verified

Height of the projectile $335665.44 m$

Step by step solution

Given information

speed of the projectile $v = 10, 000 k m / h$

Gravitational constant $G = 6.673 脳 10^{- 11} N m^{2} / k g^{2}$ ,

Mass of the earth $M = 5.9742 脳 10^{24} k g$

Radius of earth $r = 6378100 m$

Explanation

Naturally we assume that $10000 k m / h r$ is initial velocity (same as being shot from a cannon), and no air resistance. With so high a velocity, the effect of diminishing gravity with increasing radius must be taken into account, so you use an energy solution. $M$ is earth mass, $r$ is earth radius.

$\frac{K E}{m} = \frac{1}{2} {(\frac{10000 脳 1000}{3600})}^{2} = 3858025 J / k g \frac{鈭� P E}{m} = \frac{P E_{a t h e i g h t} - P E_{a t s u r f a c e}}{m} = - \frac{G M}{(r + h)} + \frac{G M}{r}$

On net energy in equilirbium,

$\frac{K E}{m} = \frac{鈭� P E}{m} \frac{K E}{m} - \frac{G M}{r} = - \frac{G M}{(r + h)} h = - \frac{G M}{(\frac{K E}{m} - \frac{G M}{r}) - r} = 335665.44 m$

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91影视

A projectile is shot straight up from the earth鈥檚 surface at a speed of $10, 000 k m / h$ . How high does it go?

Short Answer

Step by step solution

Given information

Explanation

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91影视

A projectile is shot straight up from the earth鈥檚 surface at a speed of 10,000km/h. How high does it go?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Electromagnetism

Translational Dynamics

Energy Physics

Dynamics

Electric Charge Field and Potential

Study anywhere. Anytime. Across all devices.

A projectile is shot straight up from the earth鈥檚 surface at a speed of $10, 000 k m / h$ . How high does it go?