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Chapter 1: Q71P (page 63)

A certain volcano on earth can eject rocks vertically to a maximum height H. (a) How high (in terms of H) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 m/s2; ignore air resistance on both planets. (b) If the rocks are in the air for a time T on earth, for how long (in terms of T) would they be in the air on Mars?

Short Answer

Expert verified

(a) So the volcano can throw 2.64 times the height on the earth.

(b) So the rock will stay 2.64 times time on earth.

Step by step solution

01

identification of given data

gm=3.71m/s2

02

Calculation of height

Let us consider mass of a stone is m. So the energy of the stone with which it was thrown is

Ep=mgH

Where,g=9.8m/s2

Now if the same stone is thrown in the mars, if it reaches the height Hm then the potential energy is

Ep.m=mgmHm

Now equating the above energies, we can write that

mgH=mgmHmggm=HmHHm=ggmH

Now putting the given values,

Hm=9.83.71HHm=2.64H

03

Calculation of time

Consider the time taken for the rock to reach the top is T.

By the symmetry it becomesT2

Now using kinematic equation

v=u+atv=0

Also

v=u+gT2vm=u+gmTm2

Equating both equation

gT2=gmTm2Tm=2.64T

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