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Chapter 13: Q. 15 (page 353)

An astronaut on earth can throw a ball straight up to a height of 15m. How high can he throw the ball on Mars?

Short Answer

Expert verified

The astronaut can throw a ball straight up to a height of 39.7mon Mars.

Step by step solution

01

Given information

Height on earth's surface is h=15m.

Free-fall acceleration on earth's surface: ge=9.81m/s2.

Free-fall acceleration on Mars's surface: gm=3.71m/s2.

02

Calculation

Let the mass of the ball be m.

Hence, the energy required to throw the ball to height heis:

Ee=mgehe.____(1)

Consider, he can throw the same ball to the height hmon Mars's surface.

Hence, energy required on Mars to throw the ball is :Em=mgmhm._____(2)

03

Continuation of calculation

Since, the person is same, the amount of energy he can supply to the ball is same.

Hence, compare the energies from the equation (1) and (2) :

mgehe=mgmhm⇒hm=gϵhegm.______(3)
04

Continuation of calculation

Now substitute the values to the equation (3) calculate the height.

hm=9.81m/s2(15m)3.71m/s2=39.7m.

05

Final answer

The astronaut can throw a ball straight up to a height of 39.7mon Mars.

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Most popular questions from this chapter

You have been visiting a distant planet. Your measurements have determined that the planet’s mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large.

a. What is the planet’s radius?

b. To get back to earth, you need to escape the planet. What minimum speed does your rocket need?

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