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

A projectile is shot straight up from the earth’s 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 $G = 6.673 \times 10^{- 11} N m^{2} / k g^{2}$ ,

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

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.

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

On net energy in equilirbium,

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

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A projectile is shot straight up from the earth’s 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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A projectile is shot straight up from the earth’s 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

Waves Physics

Circular Motion and Gravitation

Fields in Physics

Space Physics

Quantum Physics

Energy Physics

Study anywhere. Anytime. Across all devices.

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