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 directly South. At what angle $\theta$ (relative to due South) must the fish aim its body?

$\theta = 46.6^\circ$ West 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 constant velocity. From $t = 6$ to $t = 8$ s, it decelerates uniformly to a stop. If the particle's velocity at $t = 3$ s is $6\ \mathrm{m/s}$, what is its final position at $t = 8$ s?

Accepted Answer

$x = 32$ m

Question 2

A car passes a stationary police cruiser at a constant $30\ \mathrm{m/s}$. The cruiser waits $1$ s, then accelerates from rest at a constant rate $a$. If the cruiser catches the car at the $300$ m mark (relative to the cruiser's starting point), what is the value of $a$?

Accepted Answer

$a = 2.0\ \mathrm{m/s^2}$

Question 3

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

Accepted Answer

$v = 1.68\ \mathrm{km/s}$

Question 4

For the same person on Jupiter at latitude $65^\circ$, what is the centripetal acceleration $a_c$ due to Jupiter's rotation?

Accepted Answer

$a_c = 0.00041\ \mathrm{m/s^2}$

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 directly South. At what angle $	heta$ (relative to due South) must the fish aim its body?

Accepted Answer

$	heta = 46.6^\circ$ West of South

Question 6

Given the scenario above, what is the fish’s actual speed relative to the ground $V_{SG}$?

Accepted Answer

$V_{SG} = 16.0$ 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 required initial vertical velocity $v_{iy}$?

Accepted Answer

$v_{iy} = 2.19\ \mathrm{m/s}$

Question 8

For the same basketball shot, what is the required initial horizontal velocity $v_{ix}$?

Accepted Answer

$v_{ix} = 4.25\ \mathrm{m/s}$

Question 9

What is the magnitude of the initial velocity $v_i$ for the basketball shot described above?

Accepted Answer

$v_i = 4.80\ \mathrm{m/s}$

Question 10

What is the launch angle $	heta$ (above the horizontal) for the basketball shot?

Accepted Answer

$	heta = 23.5^\circ$

Question 11

A particle moves with constant acceleration $a = 2\ \mathrm{m/s^2}$ for $3$ s, starting from $x = -2$ m and $v_0 = 0$. What is its velocity at $t = 3$ s?

Accepted Answer

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

Question 12

A car traveling at $30\ \mathrm{m/s}$ passes a stationary police cruiser. The cruiser waits $1$ s, then accelerates at $a = 2\ \mathrm{m/s^2}$. How long after the car passes does the cruiser catch up?

Accepted Answer

$t = 15$ s

Question 13

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

Accepted Answer

$r_{eff} = 29,500$ km

Question 14

A fish swims in a river with a $16$ mph current due West. If the fish swims at $22$ mph relative to the water, what is the minimum possible speed (relative to the ground) the fish can achieve?

Accepted Answer

$6$ mph

Question 15

A basketball is thrown from $2$ m high to a hoop $9.2$ m away and $3.1$ m high, taking $1.6$ s. What is the vertical displacement $\Delta y$?

Accepted Answer

$\Delta y = 1.1$ m

Question 16

A particle decelerates uniformly from $v = 6\ \mathrm{m/s}$ to rest over $2$ s. What is its acceleration?

Accepted Answer

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

Question 17

A car passes a police cruiser at $30\ \mathrm{m/s}$. The cruiser waits $1$ s, then accelerates at $2\ \mathrm{m/s^2}$. How far has the car traveled when the cruiser catches up?

Accepted Answer

$300$ m

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