Question

Two automobiles $A$ and $B$ are approaching each other in adjacent highway lanes. At $t=0, A$ and $B$ are $3200 \mathrm{ft}$ apart, their speeds are $v_{A}=65 \mathrm{mil} / \mathrm{h}$ and $v_{B}=40 \mathrm{mi} / \mathrm{h},$ and they are at points $P$ and $Q$, respectively. Knowing that $A$ passes point $Q 40 \mathrm{s}$ after $B$ was there and that $B$ passes point $P 42$ s after $A$ was there, determine $(a)$ the uniform accelerations of $A$ and $B,(b)$ when the vehicles pass each other, $(c)$ the speed of $B$ at that time.

          Two automobiles $A$ and $B$ are approaching each other in adjacent highway lanes. At $t=0, A$ and $B$ are $3200 \mathrm{ft}$ apart, their speeds are $v_{A}=65 \mathrm{mil} / \mathrm{h}$ and $v_{B}=40 \mathrm{mi} / \mathrm{h},$ and they are at points $P$ and $Q$, respectively. Knowing that $A$ passes point $Q 40 \mathrm{s}$ after $B$ was there and that $B$ passes point $P 42$ s after $A$ was there, determine $(a)$ the uniform accelerations of $A$ and $B,(b)$ when the vehicles pass each other, $(c)$ the speed of $B$ at that time.

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Added by Phillip S.

Vector Mechanics for Engineers: Statics and Dynamics

Ferdinand P. Beer, E. Russell Johnston,… 11th Edition

Chapter 11

Instant Answer

Solved by Expert Paul Gabriel

08/17/2021

Step 1

Given: - Initial velocity of A, \(v_A = 65 \, \text{mi/h}\) or \(29.06 \, \text{m/s}\) - Initial velocity of B, \(v_B = 40 \, \text{mi/h}\) or \(17.88 \, \text{m/s}\) - Time for A to pass point Q after B was there, \(t = 40 \, \text{s}\) - Time for B to pass point Show more…

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Two automobiles $A$ and $B$ are approaching each other in adjacent highway lanes. At $t=0, A$ and $B$ are $3200 \mathrm{ft}$ apart, their speeds are $v_{A}=65 \mathrm{mil} / \mathrm{h}$ and $v_{B}=40 \mathrm{mi} / \mathrm{h},$ and they are at points $P$ and $Q$, respectively. Knowing that $A$ passes point $Q 40 \mathrm{s}$ after $B$ was there and that $B$ passes point $P 42$ s after $A$ was there, determine $(a)$ the uniform accelerations of $A$ and $B,(b)$ when the vehicles pass each other, $(c)$ the speed of $B$ at that time.

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