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Chapter 2: 19 PE (page 82)

Assume that an intercontinental ballistic missile goes from rest to a suborbital speed of 6.50 km/s in 60.0 s (the actual speed and time are classified). What is its average acceleration in m/s2 and in multiples of g (\({\bf{9}}{\bf{.80}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\))?

Short Answer

Expert verified

The acceleration of missile is \({\bf{108}}{\bf{.33}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\) or \({\bf{11}}{\bf{.05}}\,{\bf{g}}\).

Step by step solution

01

Determination of formula for average acceleration of missile

Given data:

The suborbital speed of missile is\(v = 6.50\;{\rm{km}}/{\rm{s}}\).

The initial speed of rocket is\(u = 0\).

The time for acceleration of the missile is\(t = 60\;{\rm{s}}\).

The acceleration of the missile is the increase in speed over time while moving from one position to another position.

The average acceleration of the missile is given by

\(a = \frac{{v - u}}{t}\)

Here, \(a\) is the acceleration of missile.

02

Determination of average acceleration of missile

Substitute all the values in the above equation.

\(\begin{array}{l}a = \frac{{\left( {6.50\;{\rm{km}}/{\rm{s}} - 0} \right)\left( {\frac{{1000\;{\rm{m}}}}{{1\;{\rm{km}}}}} \right)}}{{60\;{\rm{s}}}}\\a = 108.33\;{\rm{m}}/{{\rm{s}}^2}\\a = \left( {108.33\;{\rm{m}}/{{\rm{s}}^2}} \right)\left( {\frac{g}{{9.80\;{\rm{m}}/{{\rm{s}}^2}}}} \right)\\a = 11.05g\end{array}\)

Therefore, the acceleration of the missile is \(108.33\;{\rm{m}}/{{\rm{s}}^2}\) or \(11.05\,{\rm{g}}\).

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Most popular questions from this chapter

While entering a freeway, a car accelerates from rest at a rate of\({\bf{2}}{\bf{.40}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\)for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car travel in those 12.0 s? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, check your units, and discuss whether the answer is reasonable. (d) What is the car鈥檚 final velocity? Solve for this unknown in the same manner as in part (c), showing all steps explicitly.

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