Q: A fish swims in a river where the current flows due West at $16$ mph. The fish's speed relative to the water is $22$ mph. The fish wants to move so that its resultant path (relative to the ground) is pointed directly South. At what angle $\theta$ relative to the water should the fish aim?

$\theta = 47.7^\circ$ East of South

Question 1

A particle starts at $x = -2$ m. From $t = 0$ to $t = 3$ s, it accelerates at $2\ \mathrm{m/s^2}$. From $t = 3$ to $t = 6$ s, it moves at a constant velocity. From $t = 6$ to $t = 8$ s, it decelerates uniformly to a stop. What is the particle's final position at $t = 8$ s?

Accepted Answer

$x = 38\ \mathrm{m}$

Question 2

A car passes a stationary police cruiser at a constant $30\ \mathrm{m/s}$. The cruiser waits $1$ s and then accelerates at a constant rate $a$. If the cruiser catches the car at the $300$ m mark, what was the cruiser's acceleration $a$?

Accepted Answer

$a = 1.2\ \mathrm{m/s^2}$

Question 3

Jupiter has a radius of $69,600$ km and rotates once every $9.93$ hours. What is the tangential velocity $v_t$ of a person standing at a latitude of $65^\circ$?

Accepted Answer

$v_t = 2,000\ \mathrm{m/s}$

Question 4

Given the same scenario as above, what is the centripetal acceleration $a_c$ of a person standing at a latitude of $65^\circ$ on Jupiter?

Accepted Answer

$a_c = 0.058\ \mathrm{m/s^2}$

Question 5

A fish swims in a river where the current flows due West at $16$ mph. The fish's speed relative to the water is $22$ mph. The fish wants to move so that its resultant path (relative to the ground) is pointed directly South. At what angle $	heta$ relative to the water should the fish aim?

Accepted Answer

$	heta = 47.7^\circ$ East of South

Question 6

In the fish and river scenario, what is the fish’s actual speed relative to the ground $V_{SG}$?

Accepted Answer

$V_{SG} = 15.3\ \mathrm{mph}$

Question 7

A basketball is thrown from an initial height of $2$ m toward a hoop $9.2$ m away that is $3.1$ m high. If the ball takes $1.6$ s to reach the hoop, what is the magnitude of the initial velocity $v_i$?

Accepted Answer

$v_i = 7.0\ \mathrm{m/s}$

Question 8

For the basketball scenario above, what is the launch angle $	heta$ of the ball?

Accepted Answer

$	heta = 16.7^\circ$

Question 9

A police cruiser accelerates from rest after a $1$ s delay to catch a car moving at $30\ \mathrm{m/s}$. If the cruiser catches up at $300$ m, what is the time $t$ (after the car passes the cruiser) when they meet?

Accepted Answer

$t = 12.0\ \mathrm{s}$

Question 10

A particle accelerates at $2\ \mathrm{m/s^2}$ for $3$ s from $x = -2$ m. What is its velocity at $t = 3$ s?

Accepted Answer

$v = 6\ \mathrm{m/s}$

Question 11

A person stands at latitude $65^\circ$ on Jupiter. What is the effective radius $r$ of their circular path due to Jupiter's rotation?

Accepted Answer

$r = 29,470\ \mathrm{km}$

Question 12

A fish swims in a river with a $16$ mph current due West. If the fish aims $	heta$ degrees East of South so that its resultant path is due South, which vector equation best represents the scenario?

Accepted Answer

$\vec{V}_{SG} = \vec{V}_{SW} + \vec{V}_{WG}$

Question 13

A basketball is thrown from $2$ m to a hoop $9.2$ m away and $3.1$ m high in $1.6$ s. What is the vertical component of the initial velocity $v_{iy}$?

Accepted Answer

$v_{iy} = 1.81\ \mathrm{m/s}$

Question 14

A particle decelerates uniformly from $6\ \mathrm{m/s}$ to rest in $2$ s. What is the magnitude of its acceleration?

Accepted Answer

$a = -3\ \mathrm{m/s^2}$

Question 15

A car moves at $30\ \mathrm{m/s}$ and is caught by a police cruiser that starts from rest after $1$ s. If the cruiser’s acceleration is $1.2\ \mathrm{m/s^2}$, what is the distance the car travels before being caught?

Accepted Answer

$300\ \mathrm{m}$

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