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

$$300 m$$

Kinematics, Dynamics, and Rotational Motion: Step-by-Step Physics Guidance

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드