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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

Figure 13.17 showed a graph of log T versus log r for the planetary data given in Table 13.2. Such a graph is called a log-log graph. The scales in Figure 13.17 are logarithmic, not linear, meaning
that each division along the axis corresponds to a factor of 10 increase in the value. Strictly speaking, the “correct” labels on the y-axis should be 7, 8, 9, and 10 because these are the logarithms of 107...... 1010.
a. Consider two quantities u and v that are related by the expression vp = Cuq, where C is a constant. The exponents p and q are not necessarily integers. Define x = log u and y = log v. Find
an expression for y in terms of x.
b. What shape will a graph of y versus x have? Explain.
c. What slope will a graph of y versus x have? Explain.
d. Use the experimentally determined “best-fit” line in Figure 13.17 to find the mass of the sun.

a. What is the free-fall acceleration at the surface of the sun?

b. What is the free-fall acceleration toward the sun at the distance of the earth?

Two 65kgastronauts leave earth in a spacecraft, sitting 1.0mapart. How far are they from the center of the earth when the gravitational force between them is as strong as the gravitational force of the earth on one of the astronauts?

Three stars, each with the mass of our sun, form an equilateral triangle with sides 1.0 x 1012 m long. (This triangle would just about fit within the orbit of Jupiter.) The triangle has to rotate, because otherwise the stars would crash together in the center. What is the period of rotation?

Two100kglead spheres are suspended from 100-m-long massless cables. The tops of the cables have been carefully anchored exactly 1mapart. By how much is the distance between the centers of the spheres less than 1m?
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