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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